Apparatus and Method for Heating Adipose Cells

ABSTRACT

An apparatus and method for selectively heating adipose cells within a treatment region of a subject is disclosed. The method includes positioning the treatment region between first and second electrodes connected to a generator, and activating the generator to apply an alternating electric field between the first and second electrodes and across the treatment region to thereby heat the treatment region. The adipose cells heat at a faster rate than non-targets within the treatment region, which preferably results in the killing of the adipose cells.

CROSS-REFERENCE TO RELATED APPLICATIONS

Not applicable.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

Various devices have been used in the past to heat a treatment region ofan animal body for therapeutic purposes. In particular, it is known inthe art to use a radio frequency (RF) or microwave electromagnetic fieldto induce hyperthermia in an animal body for the purpose of transformingor killing certain cells of the animal body. For example, focusedmicrowave, thermotherapy has been used for breast cancer treatment, inwhich a woman's breast is placed between two compression plates and amicrowave unit positioned on each side of the breast applies anelectromagnetic field across the breast. The amplitude of theelectromagnetic field decreases as it penetrates further into the breastand, as such, the electromagnetic field is not constant throughout thethickness of the breast. Devices that utilize an electromagneticfield—whether operating at RF or microwave frequencies—do not evenlyheat the entire thickness of a treatment region and, as a result, havenot been able to achieve the desired therapeutic outcomes.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to an apparatus and method forselectively heating adipose cells within a treatment region of asubject. The method includes positioning the treatment region betweenfirst and second electrodes sized to extend across the treatment region.The first and second electrodes are connected to a generator operable toapply an alternating electric field between the electrodes. The methodfurther includes activating the generator to apply the alternatingelectric field between the first and second electrodes and across thetreatment region to thereby heat the treatment region, wherein theadipose cells heat at a faster rate than non-targets within thetreatment region. Preferably, the treatment region is heated in such amanner as to kill the adipose cells without killing the non-targetswithin the treatment region.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of an exemplary apparatus for generating analternating electric field between a single-plate top electrode and asingle-plate bottom electrode, wherein the voltage between the top andbottom electrodes is substantially constant.

FIG. 2 shows the signal generated by the apparatus of FIG. 1, whereinthe signal is substantially a sinusoid having a wavelength λ and whereina single point (designated as point X) is located at the ¼ wavelengthposition.

FIG. 3 is a diagram of an exemplary apparatus for generating analternating electric field between a top electrode comprising aplurality of tiered plates and a single-plate bottom electrode, whereinthe voltage between the top and bottom electrodes is substantiallyconstant.

FIG. 4 shows the peak of the signal generated by the apparatus of FIG.3, wherein eight points (designated as points A-H) are located at the ¼wavelength position, and wherein the peak of the sinusoid of FIG. 2 issuperimposed thereon in order to illustrate the differences between theconfigurations of the top electrodes of FIGS. 1 and 3.

FIG. 5 is a diagram of an exemplary apparatus for generating analternating electric field between a top electrode and a bottomelectrode, wherein the bottom electrode forms a bath cavity that isfilled with a flowable material that allows a substantially constantcurrent to be obtained across a treatment region of the subject.

FIG. 6 a is a diagram of an exemplary apparatus for generating analternating electric field between a top electrode and a bottomelectrode, wherein a continuous top bladder and a continuous bottombladder are attached to the top and bottom electrodes, respectively.

FIG. 6 b is a diagram of the apparatus of FIG. 6 a, wherein the top andbottom bladders are filled with a flowable material such that thebladders conform to the contours of the subject and allow asubstantially constant current to be obtained across the treatmentregion of the subject.

FIG. 7 a is a diagram of an exemplary apparatus for generating analternating electric field between a top electrode and a bottomelectrode, wherein a compartmentalized top bladder and a continuousbottom bladder are attached to the top and bottom electrodes,respectively.

FIG. 7 b is a diagram of the apparatus of FIG. 7 a, wherein the topbladder compartments and the bottom bladder are filled with variousflowable materials such that the bladders conform to the contours of thesubject and allow a substantially constant current to be obtained acrossthe treatment region of the subject.

FIG. 8 shows the temperature of ground beef liver with and withoutvarious dielectric heating modulators as a function of time.

FIG. 9 shows the temperature of ground beef liver with and withoutglucose as the dielectric heating modulator as a function of time.

FIG. 10 shows the temperature of ground beef liver and two exemplarynanogold solutions as dielectric heating modulators as a function oftime.

FIG. 11 shows the temperature of ground beef liver with and without aconcentrated gold nanoparticle solution as a function of time.

FIG. 12 shows the dissipation factor of ground beef liver mixed withconcentrated gold nanoparticle solution as a function of the amount ofthe concentrated gold nanoparticle solution.

FIG. 13 shows the temperature of a meat portion and a fat portion ofbacon as a function of time.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

The present invention is directed to an apparatus and method for heatingbiological targets of a subject through the use of dielectric heating.As used herein, the term “biological target” refers to any prokaryoticor eukaryotic cell, unicellular or multicellular microorganism,parasite, or pathogen found in a subject, including, but not limited to,bacteria, viruses, fungus, or protozoa. As used herein, the term“subject” or “body” refers to an animal such as a vertebrate, preferablya mammal (including, but not limited to, humans, murines, simians,bovines, cervids, equines, porcines, canines, and felines), and morepreferably a human. As used herein, the term “dielectric heating” refersto heating via the application of an alternating electric field(referred to herein as a “dielectric field”), preferably in the radiofrequency (RF) range. While the invention will be described in detailbelow with reference to various exemplary embodiments, it should beunderstood that the invention is not limited to the specificconfiguration or methodology of these embodiments. In addition, althoughthe exemplary embodiments are described as embodying several differentinventive features, one skilled in the art will appreciate that any oneof these features could be implemented without the others in accordancewith the invention.

In general terms, the present invention involves placing a treatmentregion of a subject between two electrodes such that the treatmentregion effectively becomes the dielectric of a capacitor. As usedherein, the term “treatment region” refers to all or a portion of asubject to be treated with dielectric heating, and includes thebiological targets and may also include non-targets. A dielectric fieldgenerated between the electrodes causes polar molecules in the treatmentregion to be attracted and repelled by the rapidly changing polarity ofthe dielectric field. The friction resulting from this molecularmovement translates into heat throughout the thickness of the treatmentregion in such a manner as to heat and kill the biological targets. Asused herein, the term “kill” in the context of a biological targetrefers to the killing, removal, or other elimination of the biologicaltarget. For example, in the context of a biological target that is acell, the term “kill” encompasses the programmed and/or unprogrammeddying of the cell by any mechanism, such as by apoptosis, necrosis,aponecrosis, autophagic degeneration, mitophagy, pexophagy, lysis,dislodging, or disruption of cell membrane, and the like.

I. Biological Targets

In general, the biological targets of the present invention include anyprokaryotic or eukaryotic cell, microorganism, parasite, or pathogenfound in a subject, including, but not limited to, bacteria, viruses,fungus, or protozoa. Thus, the present invention may be used toselectively kill many different types of biological targets within atreatment region. Among other things, the present invention finds usewith normal cells, cancerous cells, pre-cancerous cells, diseased cells,and virus-infected cells.

Thus, in one aspect, the biological targets are any of those cells foundwithin the human body, including, but not limited to, the followingtypes of cells: (1) circulatory system cells such as heart cells(myocardial cells), cells of the blood and lymph includingerythropoietin-sensitive stem cells, erythrocytes, leukocytes (e.g.,eosinophils, basophils, neutrophils (granular cells), lymphocytes, andmonocytes (agranular cells)), thrombocytes, tissue macrophages(histiocytes), organ-specific phagocytes (e.g., Kupffer cells, alveolarmacrophages, and microglia), B-lymphocytes, T-lymphocytes (e.g.,cytotoxic T cells, helper T cells, and suppressor T cells),megaloblasts, monoblasts, myeloblasts, lymphoblasts, proerythroblasts,megakaryoblasts, promonocytes, promyelocytes, prolymphocytes, earlynormoblasts, megakaryocytes, intermediate normoblasts, metamyclocytes(e.g., juvenile metamyelocytes, segmented metamyelocytes, andpolymorphonuclear granulocytes), late normoblasts, reticulocytes, andbone marrow cells; (2) muscle cells such as myofibrils, intrafusalfibers, and extrafusal fibers; (3) skeletal system cells such asosteoblasts, osteocytes, osteoclasts and their progenitor cells; (4)respiratory system cells such as capillary endothelial cells andalveolar cells; (5) urinary system cells such as nephrons, capillaryendothelial cells, granular cells, tubule endothelial cells, andpodocytes; (6) digestive system cells such as simple columnar epithelialcells, mucosal cells, acinar cells, parietal cells, chief cells, zymogencells, peptic cells, enterochromaffin cells, goblet cells, Argentaffencells, and G cells; (7) sensory cells such as auditory system cells(hair cells), olfactory system cells (olfactory receptor cells andcolumnar epithelial cells), equilibrium/vestibular apparatus cells (haircells and supporting cells), visual system cells (pigment cells),epithelial cells, photoreceptor neurons (rods and cones), ganglioncells, amacrine cells, bipolar cells and horizontal cells; (8)mesenchymal cells, stromal cells, hair cells/follicles, and adipose(fat) cells; (9) cells of simple epithelial tissues (squamousepithielium, cuboidal epithelium, columnar epithelium, ciliated columnarepithelium, and pseudostratified ciliated columnar epithelium), cells ofstratified epithelial tissues (stratified squamous epithelium(keratinized and non-keratinized), stratified cuboidal epithelium, andtransitional epithelium), goblet cells, endothelial cells of themesentery, endothelial cells of the small intestine, endothelial cellsof the large intestine, endothelial cells of the vasculaturecapillaries, endothelial cells of the microvasculature, endothelialcells of the arteries, endothelial cells of the arterioles, endothelialcells of the veins, endothelial cells of the venules, and endothelialcells of the bladder; (10) cells of connective tissue such as looseconnective (areolar) tissue including the dermis, dense fibrousconnective tissue, elastic connective tissue, reticular connectivetissue, adipose connective tissue, chondrocytes, adipose cells,periosteal cells, endosteal cells, odontoblasts, osteoblasts,osteoclasts, and osteocytes; and (11) epithelial cells such assebocytes, hair follicles, hepatocytes, type II pneumocytes,mucin-producing goblet cells, and other epithelial cells and theirprogenitors contained within the skin, lung, liver, and gastrointestinaltract. In a preferred aspect, the biological targets are adipose cells.

In another aspect, the biological targets are neoplastic cells. The term“neoplastic cells” as used herein refers to cells that result fromabnormal new growth. Neoplastic cells further include transformed cells,malignant cells or cancer cells, including blood cancers and a solidtumor (benign and malignant). As used herein, the term “tumor” refers toan abnormal mass or population of cells that result from excessive celldivision, whether malignant or benign, and all pre-cancerous andcancerous cells and tissues. A “tumor” is further defined as two or moreneoplastic cells. A “malignant tumor” is distinguished from a benigngrowth or tumor in that, in addition to uncontrolled cellularproliferation, it will invade surrounding tissues and may additionallymetastasize. The terms “transformed cells,” “malignant cells” and“cancer cells” are interchangeable and refer to cells that haveundergone malignant transformation, but may: also include lymphocytecells that have undergone blast transformation. Malignant transformationis a conversion of normal cells to malignant cells. Transformed cellshave a greater ability to cause tumors when injected into animals.Transformation can be recognized by changes in growth characteristics,particularly in requirements for macromolecular growth factors, andoften also by changes in morphology. Transformed cells usuallyproliferate without requiring adhesion to a substratum and usually lackcell to cell inhibition and pile up after forming a monolayer in cellculture. In a preferred aspect, the biological targets are cancer cellsin either solid tumor or non-solid form, including, but not limited to,those involving the following types of cancer: (1) cardiac includingsarcoma (angiosarcoma, fibrosarcoma, rhabdomyosarcoma, liposarcoma),myxoma, rhabdomyoma, fibroma, lipoma and teratoma; (2) lung includingbronchogenic carcinoma (squamous cell, undifferentiated small cell,undifferentiated large cell, adenocarcinoma), alveolar (bronchiolar)carcinoma, bronchial adenoma, sarcoma, lymphoma, chondromatoushamartoma, mesothelioma; (3) gastrointestinal including esophagus(squamous cell carcinoma, adenocarcinoma, leiomyosarcoma, lymphoma),stomach (carcinoma, lymphoma, leiomyosarcoma), pancreas (ductaladenocarcinoma, insulinoma, glucagonoma, gastrinoma, carcinoid tumors,vipoma), small bowel (adenocarcinoma, lymphoma, carcinoid tumors,Karposi's sarcoma, leiomyoma, hemangioma, lipoma, neurofibroma,fibroma), large bowel (adenocarcinoma, tubular adenoma, villous adenoma,hamartoma, leiomyoma), and other colorectal cancers; (4) genitourinarytract including kidney (adenocarcinoma, Wilm's tumor (nephroblastoma),lymphoma, leukemia), bladder and urethra (squamous cell carcinoma,transitional cell carcinoma, adenocarcinoma), prostate (adenocarcinoma,sarcoma), testis (seminoma, teratoma, embryonal carcinoma,teratocarcinoma, choriocarcinoma, sarcoma, interstitial cell carcinoma,fibroma, fibroadenoma, adenomatoid tumors, lipoma); (5) liver includinghepatoma (hepatocellular carcinoma), cholangiocarcinoma, hepatoblastoma,angiosarcoma, hepatocellular adenoma, hemangioma; (6) bone includingosteogenic sarcoma (osteosarcoma), fibrosarcoma, malignant fibroushistiocytoma, chondrosarcoma, Ewing's sarcoma, malignant lymphoma(reticulum cell sarcoma), multiple myeloma, malignant giant cell tumorchordoma, osteochronfroma (osteocartilaginous exostoses), benignchondroma, chondroblastoma, chondromyxofibroma, osteoid osteoma, andgiant cell tumors; (7) nervous system including skull (osteoma,hemangioma, granuloma, xanthoma, osteitis deformans), meninges(meningioma, meningiosarcoma, gliomatosis), brain (astrocytoma,medulloblastoma, glioma, ependymoma, germinoma (pinealoma),gliobilastoma multiform, oligodendroglioma; schwannoma, retinoblastoma,congenital tumors), spinal cord (neurofibroma, meningioma, glioma,sarcoma); (8) gynecological including uterus (endometrial carcinoma),cervix (cervical carcinoma, pre-tumor cervical dysplasia), ovaries(ovarian carcinoma (serous cystadenocarcinoma, mucinouscystadenocarcinoma, unclassified carcinoma), granulosa-thecal celltumors, Sertoli-Leydig cell tumors, dysgerminoma, malignant teratoma),vulva (squamous cell carcinoma, intraepithelial carcinoma,adenocarcinoma, fibrosarcoma, melanoma), vagina (clear cell carcinoma,squamous cell carcinoma, botryoid sarcoma (embryonal rhabdomyosarcoma)),fallopian tubes (carcinoma), breast (adenocarcinoma, lobular (smallcell) carcinoma, intraductal carcinoma, medullary breast cancer,mucinous breast cancer, tubular breast cancer, papillary breast cancer,Paget's disease, and inflammatory breast cancer); (9) hematologicincluding blood (myeloid leukemia (acute and chronic), acutelymphoblastic leukemia, chronic lymphocytic leukemia, myeloproliferativediseases, multiple myeloma, myelodysplastic syndrome). Hodgkin'sdisease, non-Hodgkin's lymphoma (malignant lymphoma); (10) skinincluding malignant melanoma, basal cell carcinoma, squamous cellcarcinoma, Karposi's sarcoma, moles dysplastic nevi, lipoma, angioma,dermatofibroma, keloids, psoriasis; and (11) adrenal glands includingneuroblastoma. Thus, the term “cancer cells” as used herein includescells afflicted by any one of the above-identified conditions.

In another aspect, the biological targets are of a pathogenic origin. Asused herein, the term “pathogen” refers to disease-causing organisms,microorganisms or agents, including, but not limited to, bacteria,viruses, or parasites. Thus, the term “biological targets” embracesbacterial cells, viruses, virally-infected cells, and parasites.

In another aspect, the biological targets are bacterium located withinthe subject. As used herein, the term “bacteria” or “bacterium” refersto all prokaryotic organisms, including those within all of the phyla inthe Kingdom Procaryotae, and is intended to encompass all microorganismsconsidered to be bacteria including Mycoplasma, Chlamydia, Actinomyces,Streptomyces, and Rickettsia. All forms of bacteria are included withinthis definition including cocci, bacilli, spirochetes, spheroplasts,protoplasts, etc. Also included within this definition are prokaryoticorganisms that are gram negative or gram positive. Thus, bacterialinfections or diseases that can be treated by the methods of the presentinvention include mycobacteria (e.g., Mycobacteria tuberculosis, M.bovis, M. avium, M. leprae, or M. africanum), rickettsia, mycoplasma,chlamydia, and legionella. Other examples of bacterial infectionscontemplated include, but are not limited to, infections caused by Grampositive bacillus (e.g., Listeria, Bacillus such as Bacillus anthracis,Erysipelothrix species), Gram negative bacillus (e.g., Bartonella,Brucella, Campylobacter, Enterobacter, Escherichia, Francisella,Hemophilus, Klebsiella, Morganella, Proteus, Providencia, Pseudomonas,Salmonella, Serratia, Shigella, Vibrio, and Yersinia species),spirochete bacteria (e.g., Borrelia species including Borreliaburgdorferi that causes Lyme disease), anaerobic bacteria (e.g.,Actinomyces and Clostridium species), Gram positive and negative coccalbacteria, Enterococcus species, Streptococcus species, Pneumococcusspecies, Staphylococcus species, Neisseria species. Specific examples ofinfectious bacteria include, but are not limited to, Helicobacterpyloris, Borelia burgdorferi, Legionella pneumophilia, Mycobacteriatuberculosis, M. avium, M. intracellulare, M. kansaii, M. gordonae,Staphylococcus aureus, Neisseria gonorrhoeae, Neisseria meningitidis,Listeria monocytogenes, Streptococcus pyogenes (Group A Streptococcus),Streptococcus agalactiae (Group B Streptococcus), Streptococcusviridans, Streptococcus faecalis, Streptococcus bovis, Streptococcuspneumoniae, Haemophilus influenzae, Bacillus antracis, corynebacteriumdiphtheriae, Erysipelothrix rhusiopathiae, Clostridium perfringers,Clostridium tetani, Enterobacter aerogenes, Klebsiella pneumoniae,Pasturella multocida, Fusobacterium nucleatum, Streptobacillusmoniliformis, Treponema pallidium, Treponema pertenue, Leptospira,Rickettsia, and Actinomyces israelli.

In another aspect, the biological targets are viruses located within thesubject. As used herein, the term “virus” refers to infectious agents,which with certain exceptions, are not observable by light microscopy,lack independent metabolism, and are able to replicate only within ahost cell. The individual particles (i.e., virions) consist of nucleicacid and a protein shell or coat; some virions also have a lipidcontaining membrane.

In another aspect, the biological targets are fungal cells locatedwithin the subject. Exemplary fungal diseases that can be treated by themethods of the present invention include, but are not limited to,aspergilliosis, crytococcosis, sporotrichosis, coccidioidomycosis,paracoccidioidomycosis, histoplasmosis, blastomycosis, zygomycosis, andcandidiasis.

In another aspect, the biological targets are parasites located withinthe subject. As used herein, the term “parasite” refers to any organismthat obtains substance or means for reproduction from an organism,whether it lives with that organism in a parasitic or symbioticrelationship. Exemplary parasitic diseases that can be treated orprevented by the methods of the present invention include, but are notlimited to, amebiasis, malaria, leishmania, coccidia, giardiasis,cryptosporidiosis, toxoplasmosis, and trypanosomiasis. Also encompassedare infections by various worms, including but not limited to,ascariasis, ancylostomiasis, trichuriasis, strongyloidiasis,toxoccariasis, trichinosis, onchocerciasis, filaria, and dirofilariasis.Also encompassed are infections by various flukes, including, but notlimited to, schistosomiasis, paragonimiasis, and clonorchiasis. Examplesof human intracellular parasites include Leishmania spp., Plasmodiumspp., Trypanosoma cruzi, Toxoplasma gondii, Babesia spp., andTrichinclla spiralis. Examples of human extracellular parasites includeEntamoeba histolytica, Giardia lamblia, Enterocytozoon bieneusi,Naegleria and Acanthamoeba, as well as most helminths. Examples ofobligate intracellular parasites include Trypanosoma rhodesiense andTrypanosoma gambiense, Isospora spp., Cryptosporidium spp, Eimeria spp.,Neospora spp., Sarcocystis spp., and Schistosoma spp.

II. Selective Killing of Biological Targets

The present invention is directed to the selective killing of biologicaltargets within a treatment region of a subject, preferably withoutsubstantially killing any non-targeted cells or organisms (collectively“non-targets”) within the subject. In order to selectively kill thebiological targets within a treatment region without substantiallykilling the non-targets, the biological targets are heated at a fasterrate than the non-targets so that the biological targets reach highertemperatures than the non-targets at the end of the dielectric heatingtreatment. The manner in which this is accomplished varies depending onthe type of the biological targets that are desired to be killed and/orthe location of the biological targets in the body. For exemplary;purposes, the following discussion involves embodiments in which thebiological targets are target cells and the non-targets are non-targetcells. As used herein, the term “target cells” refers to the cellswithin a treatment region that are targeted to be killed, withdielectric heating, and the term “non-target cells” refers to the cellswithin a treatment region that are not targeted to be killed withdielectric heating. In an exemplary embodiment, the “target cells” areneoplastic cells (cancer cells), while the non-targets cells are thenon-neoplastic cells (non-cancerous cells) in the treatment region.

A. Target Cells Naturally Heat at Faster Rate Relative to Non-TargetCells

When a treatment region is subjected to a dielectric field, the rate ofheating will vary depending on the nature of the different cell typeswithin the treatment region. As will be described in greater detailbelow, the ratio of the increase in temperature of the target cells tothe increase in temperature of the non-target cells is dependent on thedielectric constant, dissipation factor, specific heat and density ofthe cell types (assuming that the current is substantially constantacross the treatment region). As a result, in cases where the targetcells and non-target cells have dissimilar dielectric constants,dissipation factors, specific heats, and densities, or combinationsthereof, the target cells and non-target cells naturally heat atdifferent rates. For example, adipose cells naturally heat at a fasterrate than the other cells in the human body upon application of adielectric field. Thus, the adipose cells reach higher temperatures thanthe other cells in the human body at the end of the dielectric heatingtreatment such that the adipose cells may be selectively killed comparedto non-adipose cell types that heat at much lower rates.

Thus, the present invention may be used for the non-surgical removal offat from a subject such that the target cells are adipose cells. Thismay involve, for example, prominent and undesired fat deposits on theabdomen, buttocks, thighs, arms, and/or chin. Such local accumulationsof body fat (alternatively known as fat maldistribution) may result fromdisease, hormonal status, or as side effects of medication or othersubstances. Even in the absence of disease, cosmetic considerationsapply to individuals who nevertheless perceive an excess ormaldistribution of fat and wish to have it corrected.

It is contemplated that the present, invention will reduce the abnormalaccumulation of adipose cells in the abdomen, specifically in thevisceral adipose tissue compartment in subjects that have this symptom.The present invention may also be used to treat fat deposits in thedorsocervical area (“buffalo hump”), the submandibular area (“horsecollar”), the pectoral, mammary, and/or supraclavicular areas, and/orwith subcutaneous lipomas (encapsulated benign fatty tumors, single ormultiple).

Further, a dielectric heating modulator may optionally be administered,to the subject in order to further increase the rate at which theadipose cells heat compared to the non-target cells. Suitable dielectricheating modulators are discussed below. The dielectric heating modulatormay or may not have a targeting moiety specific for the target cells(i.e. the adipose cells) associated therewith. The targeting moiety maycomprise an antibody or antibody fragment that selectively binds to atarget antigen found on adipocytes. The targeting moiety specific forthe target cells is attached to the dielectric heating modulator, andthus the targeting moiety permits the selectively binding of thedielectric heating modulator to the target cells which are adiposecells.

B. Heating Rate of Target Cells Increased Relative to Non-Target Cells

In cases where the target cells and non-target, cells have similardielectric constants, dissipation factors, specific heats, anddensities, or combinations thereof, the target cells and non-targetcells naturally heat at substantially the same or similar rates. Inaccordance with the present invention, the heating rate of the targetcells relative to the non-target cells can be increased by introducinginto the treatment region a dielectric heating modulator (which may beor may not be associated with a targeting moiety) prior to theapplication of the dielectric field.

In one aspect, the net effect of the dielectric heating modulator is toincrease the heating rate of the target cells by increasing the heatgenerated within and/or transferred to the target cells. In essence, thedielectric heating modulator provides the target cells with a new higher“effective dissipation factor” by virtue of the dielectric heatingmodulator being associated with the target cells (for example, byspecific binding of the targeting moiety to a cell surface receptor,internalization, or local administration of the dielectric heatingmodulator to the target cells). If the effective dissipation factor ofthe target cells (having the dielectric heating modulator associatedtherewith) is greater than the dissipation factor of the non-targetcells (having no dielectric heating modulator associated therewith) by afactor of X, then the heating rate of the target cells will alsoincrease by a factor of X compared to the heating rate of the non-targetcells. As such, upon application of the dielectric field, the targetcells heat at a faster rate than the non-target cells such that thetarget cells may be selectively killed.

The dielectric heating modulator may be administered to the subject inany manner known to those skilled in the art. Exemplary delivery methodsinclude, but are not limited to oral, intravenous, intraperitoneal,intramuscular, rectal, intravaginal, subcutaneous, or topical. Thus, thedielectric heating modulator may be administered locally orsystemically, although the use of a targeting moiety associated with thedielectric heating modulator is preferred for systemic administration.Regardless of the delivery method, the dielectric heating modulator(with or without a targeting moiety associated therewith) is preferablyadministered in a pharmaceutically acceptable carrier, such as asolution, dispersion, or emulsion, as discussed in further detail below.

Thus, in one aspect, the dielectric heating modulator is locallyadministered to the treatment region containing the target cells. Forexample, an aqueous solution containing suspended particles of thedielectric heating modulator may be injected into the treatment-regioncontaining the target cells (e.g., a cancerous tumor) by means of aneedle and syringe. In such a case, the dielectric heating modulator isdispersed, suspended within, or otherwise absorbed or internalized bythe target cells (e.g., the cancer cells). The dielectric field is thenapplied to the treatment region containing the target cells, whereby thetarget cells heat at a faster rate than the non-target cells such thatthe target cells may be selectively killed.

In another aspect, the dielectric heating modulator is associated with atargeting moiety for systematic administration. In general, thetargeting moiety selectively binds to a target structure on or withinthe target cells, thereby selectively associating with or otherwisedelivering the dielectric heating modulator to the target cells. Once ahigh enough concentration of the dielectric heating modulator isassociated with the target cells (typically by being attached to thetarget cells or internalized therein), the dielectric field is appliedto the treatment region containing the target cells, whereby the targetcells heat at a faster rate than the non-target cells such that thetarget cells may be selectively killed. One skilled in the art willappreciate that the use of a dielectric heating modulator having atargeting moiety associated therewith may be especially useful forkilling target cells that do not manifest themselves in a localizedregion (e.g., blood cancers such as lymphoma, leukemia, and multiplemyeloma).

1. Dielectric Heating Modulator

As used herein, the term “dielectric heating modulator” refers to asubstance that, when associated with a biological target, is capable ofincreasing the heating rate of the biological target when subjected to adielectric field. Exemplary dielectric heating modulators that increasethe heating rate of a biological target include, but are not limited to,electrically conductive materials, polar materials, ionic materials, andcombinations thereof. It will also be appreciated that the dielectricheating modulator may be classified as one or more of the foregoing(e.g., a polar molecule that is also electrically conductive). Ofcourse, one skilled in the art will understand that other dielectricheating modulators may also be used in accordance with the presentinvention.

The size of the dielectric heating modulator is preferably in the micronto nanometer range. In most instances, the dielectric heating modulatorcomprises a nanoparticle. As used herein, the term, “nanoparticle” meansa particle having at least one dimension that is less than about 1micron. Preferably, the dielectric heating modulator has a particle sizeless than about 1 micron (e.g., about 900, 800, 700, 600, 500, 400, 300,200, 100 nm or less, or some range therebetween). In another aspect, theparticle size is about 1, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90 100nm, or some range therebetween. Preferably, the dielectric heatingmodulator is biologically compatible, non-immunogenic, and non-toxic tothe human body when delivered in effective amounts. The dielectricheating modulator particles may comprise spheres, rods, flakes, fibrils,discs, bars, tubes, or have an irregular shape, such as a starfishshape.

In general, it is anticipated that for a given dielectric heatingmodulator; particles of smaller size and increased surface area arepreferred. For example, for a given mass of dielectric heating modulatoradministered to a subject, it is anticipated that smaller particles(e.g., nm) are preferable to larger particles (e.g., 100 nm). Further,it is anticipated that particle shapes affect the dissipation factor ofthe dielectric heating modulator.

The effective amount of dielectric heating modulator that isadministered to a subject may readily be determined by one skilled inthe art by using the teachings discussed herein. Those skilled in theart will appreciate that the quantity of dielectric heating modulatorwill be limited by toxic or other adverse effects. However, it isanticipated that synergistic arcing effects may be observed with somedielectric heating modulators. For example, if the dielectric heatingmodulator is concentrated on a cell surface, within a cellularcompartment, or inside discrete locations of an organism (for example,in the case of a parasite that has ingested several particles of thedielectric heating modulator), current may arc between adjacentparticles or particles that are otherwise proximate to one anotherduring application of the dielectric field.

Further, it will be appreciated to those skilled in the art that theremay be some time delay between administration of the dielectric heatingmodulator (with or without a targeting moiety associated therewith) andthe application of the alternating electric field. For example, afteradministration of an effective amount of the dielectric heatingmodulator, a time delay of seconds up to hours may occur prior toapplication of the alternating electric field, for example about 5, 10,30, 46, 60 seconds, 1, 2, 5, 10, 15, 25, 30, 35, 40, 45, 50, 55, 60minutes; 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6 hours. The time delaywill generally depend on the nature of the dielectric heating modulator,the nature of the targeting moiety, the amount of the dielectric heatingmodulator, and the route of administration.

In one aspect, the dielectric heating modulator comprises anelectrically conductive material. As used herein, the term “electricallyconductive material” refers to any material that is capable ofconducting electrical current. For example, the electrically conductivematerial may comprise electroconductive metal particles, such asparticles of nickel, iron, copper, zinc, chromium, cobalt, aluminum,silver, gold, iridium, platinum, palladium, zirconium, tin, and thelike, as well as particles of alloys of at least two of such metalswhich exhibit electroconductivity. The metal particles can be in theform of powders, fibers, or flakes. The electrically conductive materialmay also comprise one or more metal salts, metal oxides, metal colloids,or other metal complexes. Inorganic metal salts include, for example,chlorides, sulfates, and nitrates of these metals (e.g., iron sulfate,copper sulfate, and/or magnesium sulfate). Organic metal salts include,for example, acetates and formates of these metals. Metal complexesinclude those with bidentate, tridentate, or tetradentate ligand.Exemplary ligands include organic molecules, such as salens,metalloporphyrin, phthalocyanine, macrocyclic teraaza, and cyclam-typeligand systems.

For example, suitable iron salts include, but are not limited to, ferrichypophosphite, ferric albuminate, ferric chloride, ferric citrate,ferric oxide saccharate, ferric ammonium citrate, ferrous chloride,ferrous gluconate, ferrous iodide, ferrous sulfate, ferrous lactate,ferrous fumarate, heme, ferric trisglycinate, ferrous bisglycinate,ferric nitrate, ferrous hydroxide saccharate, ferric sulfate, ferricgluconate, ferric aspartate, ferrous sulfate heptahydrate, ferrousphosphate, ferric ascorbate, ferrous formate, ferrous acetate, ferrousmalate, ferrous glutamate, ferrous cholinisocitrate, ferroglycinesulfate, ferric: oxide hydrate, ferric pyrophosphate soluble, ferrichydroxide saccharate, ferric manganese saccharate, ferric subsulfate,ferric ammonium sulfate, ferrous ammonium sulfate, ferricsesquichloride, ferric choline citrate, ferric manganese citrate, ferricquinine citrate, ferric sodium citrate, ferric sodium edetate, ferricformate, ferric ammonium oxalate, ferric potassium oxalate, ferricsodium oxalate, ferric peptonate, ferric manganese peptonate, ferricacetate, ferric fluoride, ferric phosphate, ferric pyrophosphate,ferrous pyrophosphate, ferrous carbonate saccharated, ferrous carbonatemass, ferrous succinate, ferrous citrate, ferrous tartrate, ferricfumarate, ferric succinate, ferrous hydroxide, ferrous nitrate, ferrouscarbonate, ferric sodium pyrophosphate, ferric tartrate, ferricpotassium tartrate, ferric subcarbonate, ferric glycerophosphate, ferricsaccharate, ferric hydroxide saccharate, ferric manganese saccharate,and ferrous ammonium sulfate, ferric sodium pyrophosphate, ferrouscarbonate, ferric hydroxide, ferrous oxide, ferric oxyhydroxide, andferrous oxalate.

Examples of suitable iron complexes include, but are not limited to,polysaccharide-iron complex, methylidine-iron complex,ethylenediaminetetraacetic acid (EDTA)-iron complex, phenanthrolene ironcomplex, p-toluidine iron complex, ferrous saccharate complex,ferrlecit, ferrous gluconate complex, ferrum vitis, ferrous hydroxidesaccharate complex, iron-arene sandwich complexes, acetylacetone ironcomplex salt, iron-dextran complex, iron-dextrin complex,iron-sorbitol-citric acid complex, saccharated iron oxide, ferrousfumarate complex, iron porphyrin complex, iron phtalocyamine complex,iron cyclam complex, dithiocarboxy-iron complex, desferrioxamine-ironcomplex, bleomycin-iron complex, ferrozine-iron complex, ironperhaloporphyrin complex, alkylenediamine-N,N-disuccinic acid iron(III)complex, hydroxypyridone-iron(III) complex, aminoglycoside-iron complex;transferrin-iron complex, iron thiocyanate complex, iron complexcyanides, porphyrinato iron(III) complex, polyaminopolycarbonate ironcomplexes, dithiocarbamate iron complex, adriamycin iron complex,anthracycline-iron complex, N-methyl-D-glucamine dithiocarbamate(MGD)-iron complex, ferrioxamine B, ferrous citrate complex, ferroussulfate complex, ferric gluconate complex, ferrous succinate complex,polyglucopyranosyl iron complex; polyaminodisuccinic acid iron complex,biliverdin-iron complex, deferiprone iron complex, ferricoxyhydride-dextran complex, dinitrosyl dithiolato iron complex, ironlactoferrin complexes, 1,3-ethylenediaminetetraacetic acid (EDTA) ferriccomplex salts, diethylenetriaminepentaacetic acid iron complex salts,cyclohexanediaminetetraacetic acid iron complex salts,methyliminodiacetic acid iron complex salts, glycol etherdiaminetetraacetic acid iron complex salts, ferric hydroxypyronecomplexes, ferric succinate complex, ferric chloride complex, ferricglycine sulfate complex, ferric aspartate complex, sodium ferrousgluconate complex, and ferrous hydroxide polymaltose complex.

Examples of suitable copper salts and complexes include, but are notlimited to, copper sulfate (cupric sulfate), copper nitrate, copperphosphate, copper fluoride, copper gluconate, copper chelate, copperhistadyl chelate, copper peptide chelate, copper EDTA, copper EGTA,cupric acetate, cupric borate, cupric bromide, cupric butyrate, cupriccarbonate, cupric chlorate, cupric chloride, cupric chromate, cupriccitrate, cupric formate, cupric glycinate, cupric hydroxide, cupricnitrate, cupric oleate, cupric oxalate, cupric oxide, cupricperchlorate, cupric phosphate, cupric salicylate, cupric selenate,cupric stearate, cupric sulfide, cupric tartrate, cuprous acetate,cuprous borate, cuprous bromide, cuprous butyrate, cuprous carbonate,cuprous chlorate, cuprous chloride, cuprous chromate, cuprous citrate,cuprous formate, cuprous glycinate, cuprous hydroxide, cuprous iodide,cuprous nitrate, cuprous oleate, cuprous oxalate, cuprous oxide, cuprousperchlorate, cuprous phosphate, cuprous salicylate, cuprous selenate,cuprous stearate, cuprous sulfide, and cuprous tartrate.

Examples of suitable silver salts include, but are not limited to,silver acetate, silver borate, silver bromide, silver butyrate, silvercarbonate, silver chlorate, silver chloride, silver chromate, silvercitrate, silver formate, silver glycinate, silver hydroxide, silveriodide, silver nitrate, silver oleate, silver oxalate, silver oxide,silver perchlorate, silver phosphate, silver salicylate, silverselenate, silver stearate, silver sulfide, and silver tartrate.

Examples of suitable gold salts include, but are not limited to, goldacetate, gold borate, gold bromide, gold butyrate, gold carbonate, goldchlorate, gold chloride, gold chromate, gold citrate, gold formate, goldglycinate, gold hydroxide, gold iodide, gold hitrate, gold oleate, goldoxalate, gold oxide, gold perchlorate, gold phosphate, gold salicylate,gold selenate, gold stearate, gold sulfide, and gold tartrate.

Examples of suitable aluminum salts include, but are not limited to,aluminum-acetate, aluminum borate, aluminum bromide, aluminum butyrate,aluminum carbonate, aluminum chlorate, aluminum chloride, aluminumchromate, aluminum citrate, aluminum-formate, aluminum glycinate,aluminum hydroxide, aluminum iodide, aluminum nitrate, aluminum oleate,aluminum oxalate, aluminum oxide, aluminum perchlorate, aluminumphosphate, aluminum salicylate, aluminum selenate, aluminum stearate,aluminum sulfide, and aluminum tartrate.

The dielectric heating modulator may also comprise an electricallyconductive material that is an electrocatalyst nanoparticle. In general,the electrocatalyst is comprised of a metallic catalytic material and acarbon particle. The carbon particle is comprised of a material thatsupports the metallic catalytic material, such as acetylene black (DenkaBlack® available from Denki Kagaku Kogyo K.K.), Vulcan XC72 (availablefrom Cabot Corporation), ketjen black, amorphous carbon, carbonnanotube, and carbon nanohorn. A preferred electrocatalyst is theDynalyst family of electrocatalysts (available from Cabot Corporation),particularly Dynalyst 50KR1 which is 50% Pt/ketjen black.

Non-metallic electrically conductive materials are also suitable foruse, in accordance with the present invention, such as Black pearl 2000(available from Cabot Corporation) which has a large surface area andthose described in carbon particles described above, as well as Gannonet al., Carbon nanotube-enhanced thermal destruction of cancer cells ina noninvasive radiofrequency field, Cancer. Dec. 15, 110 (12) 2654-65(2007); Gannon et al., Intracellular gold nanoparticles enhancenon-invasive radiofrequency thermal destruction of humangastrointestinal cancer cells, Nanobiotechnology, Jan. 30, 6:2 (2008);and U.S. Pat. No. 4,303,636. Thus, electrically conductive materialscomprising carbon include all-types of conductive carbon blacks, many ofwhich are known in the art. Carbon nanofibers and nanotubes are alsosuitable for use and can have any suitable surface area or aspect ratio,but typically will have an aspect ratio of about 25 or more (e.g., about25 to about 250, or about 50 to about 150).

In another aspect, the dielectric heating modulator comprises a polarmaterial. As used herein, the terms “polar molecule” or “polar material”refer to an electrically neutral molecule that exhibits non-zeroelectric dipole moment caused by significant electron shift in at leastone covalent bond related to the same molecule. Exemplary polarmaterials have functional groups selected from carboxyl, hydroxyl,ester, carbonyl, ether, nitrile, amine, amide, and halogen groups.Exemplary polar molecules include water-soluble polymers such aspolyvinylpyrrolidone, polyethylene oxide, polyalkylene glycol(especially polyethylene glycol), and the like, as well as water-solublepolydextrose, saccharides and polysaccharides, such as pullulan,dextran, sucrose, glucose, lactose, maltose, xylose, arabinose, ribose,fructose, mannitol, mannose, galactose, sorbitol and the like. Otherexamples of polar materials include monohydric and polyhydric alcoholsand amines, such as ethanol and triethanol amine. The polar material mayhave a lactam group, preferably substituted and unsubstituted 4 to 7membered lactam rings. Suitable substituents include C1-3 alkyl groupsand aryl groups. Preferred lactams include substituted and unsubstituted4 to 6 membered lactams and most preferably unsubstituted 4 to 6membered lactams. Examples of suitable lactams include N-vinyllactamssuch as N-vinyl-2-pyrrolidone, N-vinyl-2-piperidone,N-vinyl-2-caprolactam, N-vinyl-3-methyl-2-pyrrolidone,N-vinyl-3-methyl-2-piperidone, N-vinyl-3-methyl-2-caprolactam,N-vinyl-4-methyl-2-pyrrolidone, N-vinyl-4-methyl-2-caprolactam,N-vinyl-5-methyl-2-pyrrolidone, N-vinyl-5-methyl-2-piperidone,N-vinyl-5,5-dimethyl-2-pyrrolidone,N-vinyl-3,3,5-trimethyl-2-pyrrolidone,N-vinyl-5-methyl-5-ethyl-2-pyrolidone,N-vinyl-3,4,5-trimethyl-3-ethyl-2-pyrrolidone,N-vinyl-6-methyl-2-piperidone, N-vinyl-6-ethyl-2-piperidone,N-vinyl-3,5-dimethyl-2-piperidone, N-vinyl-4,4-dimethyl-2-piperidone,N-vinyl-7-methyl-2-caprolactam, N-vinyl-7-ethyl-2-caprolactam,N-vinyl-3,5-dimethyl-2-caprolactam, N-vinyl-4,6-dimethyl-2-caprolactam,N-vinyl-3,5,7-trimethyl-2-caprolactam, N-vinylmaleimide,vinylsuccinimide, mixtures thereof and the like. Preferred lactamsinclude heterocyclic monomers containing 4 carbon atoms in theheterocyclic ring. A highly preferred vinyllactam isN-vinyl-2-pyrrolidone.

Preferred polar molecules are those that are naturally occurringmolecules in the body or mimics thereof, such as glucose, glucosemimics, and their metabolites. A preferred polar molecule is2-deoxyglucose and its derivatives. Such compounds are preferentiallytaken up by cancer cells, and thus are well-suited for use in thepresent invention when the biological targets are cancer cells.

In another aspect, the dielectric heating modulator comprises an ionicmaterial. The term “ionic material” refers to those materials with atleast one charge on the molecule, for example anionic (negativelycharged), cationic (positively charged), or zwitterionic (bothpositively and negatively charged) compounds. Ionic materials includeacids, bases, and salts. Exemplary ionic materials include amino acids,proteins, and nucleic acids. Exemplary acids comprise at least onecarboxylic acid, phosphoric acid or sulphonic acid functional group.Exemplary bases include sodium hydroxide and potassium hydroxide.Exemplary salts include metal salts, such as aluminum oxidelithiumcarbonate, sodium chloride, sodium bromide, potassium chloride,potassium sulfate, potassium phosphate, sodium acetate, sodium citrate,and the like.

2. Targeting Moiety

The dielectric heating modulator may also be associated with a targetingmoiety. As used herein, the term “targeting moiety” refers to asubstance, means, or technique of selectively delivering the dielectricheating modulator to the biological targets (compared to thenon-targets). The targeting moiety may be directly linked or indirectlyassociated with the dielectric heating modulator. In most instances, thedielectric heating modulator is conjugated to the targeting moiety, forexample by a covalent bond. The targeting moiety could also beindirectly associated with the dielectric heating modulator, for exampleif the targeting moiety forms part of a liposome or other carrier forthe dielectric heating modulator. Preferably, the targeting moiety isbiologically compatible and non-toxic to the human body.

In one aspect, the targeting moiety interacts with a target structure onor within the biological target. In general, target structurescontemplated by the present invention that interact with and/orselectively bind to the targeting moiety include, but are not limitedto, cell surface proteins, cell surface receptors, cell surfacepolysaccharides, extracellular matrix proteins, intracellular proteins,intracellular nucleic acids, and the like. In some cases, the targetstructure is located on the surface of a cell (e.g., cancer cells). Inother cases, the target structure is located within the cell (e.g.,nucleic acids). The range of target structures is virtually unlimited.Indeed, any inter-biological or intra-biological feature (e.g.,glycoprotein) of a cell or tissue is encompassed as a target structurewithin the present invention. For example, target structures may includeepitopes selected from a viral coat protein, a bacterial cell wallprotein, or a viral or bacterial polysaccharide.

In another aspect, the targeting moiety-selectively, binds to a targetstructure that is a tumor-associated antigen on the cancer cell. Tumorassociated antigens include, but are not limited to, products of mutatedoncogenes and tumor suppressor genes, products of other mutated genes,overexpressed or aberrantly expressed cellular proteins, tumor antigensproduced by oncogenic viruses, oncofetal antigens, altered cell surfaceglycolipids and glycoproteins, and cell type-specific differentiationantigens. In one example, the tumor associated antigen is selected fromthe group consisting of tumor associated glycoprotein-72 (TAG-72, apancarcinoma antigen, Kjeldsen et al., Preparation and Characterizationof Monoclonal Antibodies Directed to the Tumor-associated O-linkedSialosyl-2→6α-N-Acetylgalactosaminyl (Sialosyl-Tn) Epitope, Cancer Res.48 2214-2220 (1988); U.S. Pat. No. 5,892,020; U.S. Pat. No. 5,892,019;and U.S. Pat. No. 5,512,443), tumor associated antigens human carcinomaantigen (U.S. Pat. No. 5,693,763; U.S. Pat. No. 5,545,530; and U.S. Pat.No. 5,808,005); TP1 and TP3 antigens from osteocarcinoma cells (U.S.Pat. No. 5,855,866); Thomsen-Friedenreich (TF) antigen fromadenocarcinoma cells (U.S. Pat. No. 5,110,911); KC-4 antigen from humanprostrate adenocarcinoma (U.S. Pat. No. 4,708,930 and U.S. Pat. No.4,743,543); a human colorectal cancer antigen (U.S. Pat. No. 4,921,789);CA125 antigen from cystadenocarcinoma (U.S. Pat. No. 4,921,790); DF3antigen from human breast carcinoma (U.S. Pat. No. 4,963,484 and U.S.Pat. No. 5,053,489); a human breast tumor antigen (U.S. Pat. No.4,939,240); p97 antigen of human melanoma (U.S. Pat. No. 4,918,164);carcinoma or orosomucoid-related antigen (CORA) (U.S. Pat. No.4,914,021); a human pulmonary carcinoma antigen that reacts with humansquamous cell lung carcinoma but not with human small cell lungcarcinoma (U.S. Pat. No. 4,892,935); T and Tn haptens in glycoproteinsof human breast carcinoma (Springer et al., Blood group Tn-activemacromolecules from human carcinomas and erythrocytes: Characterizationof and specific reactivity with mono-and poly-clonal anti-Tn antibodiesinduced by various immunogens, Carbohydr. Res. 178 271-292 (1988)), MSAbreast carcinoma glycoprotein (Tjandra et al., Application of mammaryserum antigen assay in the management of breast cancer: A preliminaryreport, British J. Surgery 75 811-817 (1988)); MFGM breast carcinomaantigen (Ishida et al., Related Glycoproteins from Normal Secretory andMalignant Breast Cells: Purification and Initial ComparativeCharacterizations, Tumor Biol., 10 12-22 (1989)); DU-PAN-2 pancreaticcarcinoma antigen (Lan et al., Isolation and Properties of a HumanPancreatic Adenocarcinoma-associated Antigen, DU-PAN-21, Cancer Res. 45305-310 (1985)); CA-125 ovarian carcinoma antigen (Hanisch et al.,Structural studies on oncofetal carbohydrate antigens (Ca 19-9, Ca 50,and Ca 125) carried by O-linked sialyl-oligosaccharides on humanamniotic mucins, Carbohydr. Res. 178 29-47 (1988)); YH206 lung carcinomaantigen (Hinoda et al., Immunochemical characterization ofadenocarcinoma-associated antigen yh206, Cancer J. 42 653-658 (1988)),alphafetoprotein (AFP), carcioembryonic antigen (CEA), MUC-1 (breastcancer), melanoma-associate antigens (MAGE), carbohydrate antigen 19-9(CA19.9), prostate specific antigen (PSA), and B melanoma antigen(BAGE). The targeting moiety may also target the products of oncogenesor tumor suppressors. Oncogene products include, but are not limited to,tyrosine kinases, both membrane-associated and cytoplasmic forms, suchas members of the Src family, serine/threonine kinases, such as Mos,growth factor and receptors, such as platelet derived growth factor(PDDG), SMALL GTPases (G proteins) including the ras family,cyclin-dependent protein kinases (cdk), members of the myc familymembers including c-myc, N-myc, and L-myc, and bcl-2 and family members.Thus, examples of oncogene products include, but are not limited to, asras, src, abl, fgr, rel, yes, fes, net, mos, raf, erb B, erb A, fms,neu, ros, kit, sea, sis, myc, myb, fos, ski, jun and ets. Examples oftumor suppressors include, but are not limited to, Muc 1, CCAM, RB, APC,DCC, MEN-I, MEN-II, zac1, MMAC1, FCC, MCC p16, p21, p27, p53, p73, zac1,MMAC1, Rb, Wilms tumor (WT-1), DCC, neurofibromatosis type 1 (NF-1),NF-2, von Hippel-Lindau (VHL) disease tumor suppressor, Maspin, Brush-1,BRCA-1, BRCA-2, the multiple tumor suppressor (MTS), gp95/p97 antigen ofhuman melanoma, renal cell carcinoma-associated G250 antigen, KS ¼pan-carcinoma antigen, ovarian carcinoma antigen (CA125), prostate:specific antigen, melanoma antigen gp75, CD9, CD63, CD53, CD37, CD63,R2, CD81, CO029, TI-1, L6 and SAS. Of course, these are merely exemplaryoncogene products and tumor suppressors and it is envisioned that thepresent invention may be used in conjunction with other types of agentsthat are known to those skilled in the art.

The present invention is not limited to any particular targeting moiety.Indeed, a variety of targeting moieties are contemplated by theinvention. Examples of targeting moieties include, but are not limitedto, nucleic acids (e.g., RNA and DNA), polypeptides (e.g., receptorligands, signal peptides, avidin, Protein A, antigen binding proteinsfusion proteins, etc.), polysaccharides, biotin, hydrophobic groups,hydrophilic groups, drugs, and any organic molecules that bind toreceptors. Exemplary targeting moieties are also described in U.S.Patent Application No. 2007/0248537, U.S. Pat. No. 7,329,638, and U.S.Pat. No. 7,5210,555.

In one aspect, the targeting moiety is an antibody or antibody fragment.In general, the term “antibody” refers to immunoglobulin molecules andimmunologically active portions of immunoglobulin molecules (moleculesthat contain an antigen binding site that specifically binds anantigen), including monoclonal antibodies (e.g., full length monoclonalantibodies), polyclonal antibodies, multispecific antibodies e.g.,bispecific antibodies), chimeric antibodies. CDR-grafted antibodies,humanized antibodies, human antibodies, and single chain antibodies(scFvs). The term “monoclonal antibody” or “monoclonal antibodycomposition” refers to a population of antibody molecules that containonly one species of an antigen binding site capable of recognizing andbinding to a particular epitope of a target antigen. A monoclonalantibody composition typically displays a single binding specificity andaffinity for a particular target antigen with which it immunoreacts. Theterm “single-chain antibody” refers to a protein having atwo-polypeptide chain structure consisting of a heavy and a light chain,said chains being stabilized, for example, by interchain peptidelinkers, which has the ability to specifically bind antigen. Techniquesfor producing single chain antibodies specific to target antigen aredescribed, for example, in U.S. Pat. No. 4,946,778.

The term “antibody fragment” refers to F(ab′)2 fragments, Fab fragments,Fab′ fragments, Fd fragments, Fv fragments, and single domain antibodyfragments (DAbs). Immunologically active portions of immunoglobulinsinclude, for example, F(ab) and F(ab′)2 fragments. Methods for theconstruction of Fab fragments are described, for example, in Huse, etal. Generation of a large combinatorial library of the immunoglobulinrepertoire in phage lambda. Science 246 1275-1281 (1989). Other antibodyfragments may be produced by techniques known in the art, including, butnot limited to: (1) an F(ab′)2 fragment produced by pepsin digestion ofan antibody molecule; (2) a Fab fragment generated by reducing thedisulfide bridges of an F(ab′)2 fragment; (3) a Fab′ fragment generatedby the treatment of the antibody molecule with papain and a reducingagent; and (4) Fv fragments. Various antibody fragments can also beproduced by art-recognized recombinant engineering techniques. Non-humanantibodies can be “humanized” by techniques described, for example, inU.S. Pat. No. 5,225,539. In one method, the non-human CDRs are insertedinto a human antibody or consensus antibody framework sequence. Furtherchanges can then be introduced into the antibody framework to modulateaffinity or immunogenicity.

As discussed above, in one aspect, the targeting moiety recognizes atarget structure which is a tumor-associated antigen that is foundspecifically on neoplastic cells and not on normal cells. In a preferredexample, the targeting moiety is an antibody or antibody fragment thatspecifically recognizes cancer cells but does not recognize normal,non-cancerous cells. As a specific example, the targeting moiety mayselectively bind to Ep-CAM (Epithelial Cell Adhesion Molecule), alsoknown as 17-1A, KSA, EGP-2, and GA733-2. Ep-CAM is a transmembraneprotein that is highly expressed in many solid tumors, includingcarcinomas of the lung, breast, ovary, colorectum, and squamous cellcarcinoma of the head and neck, but weakly expressed in most normalepithelial tissues. Accordingly, the invention provides for a targetingmoiety associated with a dielectric heating modulator in which thetargeting moiety selectively binds to Ep-CAM on the cancer cell. In aspecific example, the targeting moiety comprises an antibody or antibodyfragment that binds to the extracellular domain of human Ep-CAM. Thetargeting moiety may be joined directly to the dielectric heating,modulator or through a linker. In one embodiment, the linker is apeptide linker or a chemical linker. Methods for linking a dielectricheating modulator, such, as gold nanoparticles, to a targeting moiety,such as antibodies, are known in the literature. See generally Glazer etal., Radiofrequency field-induced thermal cytotoxicity in cancer cellstreated with fluorescent nanoparticle., Cancer. 116 (13) 3285-3293(2010); Curley et al., Noninvasive radiofrequency field-inducedhyperthermic cytotoxicity in human cancer cells using cetuximab-targetedgold nanoparticles, J Exp Ther. Oncol. 7 (4) 313-326 (2008). Methods forlinking gold nanoparticles to 2-deoxyglucose are described in Aydogan etal., AuNP-DG: Deoxyglucose-Labeled Gold Nanoparticles as X-ray ComputedTomography. Contrast Agents for Cancer Imaging, Mol Imaging Biol. 2010October; 12 (5):463-7 and Li et al., A novel functional CT contrastagent for molecular imaging of cancer, Phs. Med. Biol, 55, 4389-4397(2010). It will be appreciated to those skilled in the art that othertargeting moiety-dielectric heating modulator conjugates may be producedin which the anti-Ep-CAM antibody is replaced with another antibody orantibody fragment specific for another tumor associated antigen.

In yet another example, the targeting moiety comprises peptides thatbind specifically to the target cells, such as tumor blood vessels (seee.g., Arap et al., Cancer treatment by targeted drug delivery to tumorvasculature in a mouse model, Science 279 377-80 (1998)). These peptidesinclude, but are not limited to, peptides containing the RGD(Arg-Gly-Asp) motif, the NGR (Asn-Gly-Arg) motif, or the GSL(Gly-Ser-Leu) motif. These peptides and conjugates containing thesepeptides selectively bind to various tumors, including, but not limitedto, breast carcinomas, Karposi's sarcoma, and melanoma. It is notintended that the present invention be limited to a particular mechanismof action. Indeed, an understanding of the mechanism is not necessary tomake and use the present invention. However, it is believed that thesepeptides are ligands for integrins and growth factor receptors that areabsent or barely detectable in established blood vessels.

The targeting moiety may also be a “disease: receptor targeting ligand,”which includes agents exploited for their ability to bind to certaincellular receptors that are overexpressed in disease states, such ascancer, neurological diseases, and cardiovascular diseases. Examples ofsuch receptors which are targeted include estrogen receptors, amino acidtransporters, androgen receptors, pituitary receptors, transferrinreceptors, progesterone receptors, and glucose transporters.Non-limiting examples of agents that can be applied as disease-receptortargeting ligands include androgen, estrogen, somatostatin,progesterone, transferrin, luteinizing hormone, and luteinizing hormoneantibody. Disease receptor targeting ligands (e.g., pentetreotide,octreotide, transferrin, and pituitary peptide) bind to cell receptors,some of which are overexpressed on certain cells.

In another example, the targeting moiety comprises glucose or a glucosemimic. Glucose transporters are overexpressed in various diseased cellssuch as certain cancerous cells. Tetraacetate mannose, deoxyglucose,certain polysaccharides (e.g., neomycin, kanamycin, tobramycin), andmonosaccharides (e.g., glucosamine) also bind the glucose transporterand may be used as disease receptor targeting ligands. Thus, thetargeting moiety may be a mimic glucose selected from the groupconsisting of deoxyglucose, glucosamine, tetraacetylated glucosamine,neomycin, kanamycin, gentamycin, paromycin, amikacin, tobramycin,netilmicin, ribostamycin, sisomicin, micromicin, lividomycin, dibekacin,isepamicin, astromicin, and aminoglycoside. Similarly, amino acidtransporters are also overexpressed in various diseased cells such ascertain cancerous cells. As such, amino acids and/or amino acidderivatives (e.g., serine, tyrosine, alpha methyltyrosine) may be usedas targeting moieties.

The folate receptor is included herein as another example of a diseasereceptor. Folate receptors (FRs) are overexposed on many neoplasticcell-types (e.g., lung, breast, ovarian, cervical, colorectal,nasopharyngeal, renal adenocarcinomas, malignant melanoma, andependymomas), but primarily express several normal differentiatedtissues (e.g., choroid plexus, placenta, thyroid, and kidney) (Weitmanet al., Distribution of the folate receptor GP38 in normal and malignantcell lines and tissues, Cancer Res. 52 3396-3401 (1992); Campbell etal., Folate-binding protein is a marker for ovarian cancer” Cancer Res.51 5329-5338 (1991); Weitman et al., Cellular localization of the folatereceptor: potential role in drug toxicity and folate homeostasis, CancerRes. 52 6708-67111 (1992); Holm et al., Folate receptor of human mammaryadenocarcinoma, APMIS 102 413-419 (1994); Ross et al., Differentialregulation of folate receptor isoforms in normal and malignant tissue invivo and in established cell lines, Cancer 73 2432-2443 (1994); Franklinet al., New anti-lung-cancer antibody cluster 12 reacts with humanfolate receptors present on adenocarcinoma, Int. J. Cancer-Supplement 889-95, (1994); Weitman et al., The folate receptor in central nervoussystem malignancies of childhood, J. Neuro-Oncology 21 107-112 (1994)).Folate receptors have been used to deliver folate-conjugated proteintoxins, drug/antisense oligonucleotides and liposomes into tumor cellsoverexpressing the folate receptors (Ginobbi et al., Folicacid-polylysine carrier improves efficacy of c-myc antisenseoligodeoxynucleotides on human melanoma (M14) cells, Anticancer Res. 1729-35 (1997); Leamon et al., Delivery of macromolecules into livingcells: a method that exploits folate receptor endocytosis, Proc. Natl.Acad. Sci. 88 5572-5576 (1991); Leamon et al., Cytotoxicity ofmomordin-folate conjugates in cultured human cells, J. Biol. Chem. 26724966-24971 (1992); Leamon et al., Cytotoxicity of folate-pseudomonasexotoxin conjugates toward tumor cells, J. Biol. Chem. 268 24847-24854(1993); Lee et al., Delivery of liposomes into cultured KB cells viafolate receptor-mediated endocytosis, J. Biol. Chem. 269 3198-3204(1994)). Further, bispecific antibodies that contain anti-FR antibodieslinked to anti-T cell receptor antibodies have been used to target Tcells to FR-positive, tumor cells and are currently in clinical trialsfor ovarian carcinomas (Canevari et al., Ovarian carcinoma therapy withmonoclonal antibodies, Hybridoma 12 501-507 (1993); Bolhuis et al.,Adoptive immunotherapy of ovarian carcinoma with Bs-MAb targetedlymphocytes. A multicenter study, Int. J. Cancer 7 78-81 (1992); Patricket al., Folate receptors as potendal therapeutic targets in choroidplexus tumors of SV40 transgenic mice, J. Neurooncol. 32 111-123,(1997); Coney et al., Chimeric murine-human antibodies directed againstfolate binding receptor are efficient mediators of ovarian carcinomacell killing, Cancer Res. 54 2448-2455 (1994); Kranz et al., Conjugatesof folate and anti-T-cell-receptor antibodies specifically targetfolate-receptor-positive tumor cells for lysis, Proc. Natl. Acad. Sci.92 9057-9061 (1995)).

Thus, in another aspect, the targeting moieties comprise folate receptortargeting ligands, such as folic acid and analogs of folic acid. Incertain embodiments, a folate receptor targeting ligand is selected fromthe group consisting of folate, folic acid, methotrexate, and tomudex.Folic acid as well as antifolates such as methotrexate enter into cellsvia high affinity folate receptors (glycosylphosphatidylinositol-linkedmembrane folate-binding protein) in addition to classical reduced-folatecarrier system (Westerhof et al., Membrane transport of natural folatesand antifolate compounds in murine L1210 leukemia cells: Role ofcarrier-and receptor-mediated transport systems, Cancer Res. 515507-5513 (1991); Orr et al., Similarity of folate receptor expressionin UMSCC 38 cells to squamous cell carcinoma differentiation markers, J.Natl. Cancer inst. 87 299-303 (1995); Hsuch et. al., Alteredfolate-binding protein mRNA stability in KB cells grown infolate-deficient medium,” Biochem. Pharmacol. 45 2537-2545 (1993)).

In addition, the present invention contemplates that vitamins (both fatsoluble and non-fat soluble vitamins) may be used as targeting moietiesto target biological targets that have receptors for, or otherwise takeup, these vitamins. Particularly preferred for this aspect of theinvention are the fat soluble vitamins, such as vitamin D and itsanalogues, vitamin. E, Vitamin A, and the like or water soluble vitaminssuch as Vitamin C, and the like.

In another example, the targeting moiety is a signal peptide. Thesepeptides are chemically synthesized or cloned, expressed and purified asknown in the art. Signal peptides are used to target an electricallyconductive material to a discrete region within a cell. In still otherembodiments, a signal peptide is provided in addition to a targetingmoiety that is responsible for targeting the drug delivery component toa target cell or tissue (e.g., a cancer cell). In some embodiments,specific amino acid sequences in proteins are responsible for targetingthe dielectric heating modulator into cellular organelles andcompartments.

In another aspect, the targeting moiety is an anaerobic bacteria havingthe dielectric heating modulator either internalized therein or attachedthereto or can be used as a gene delivery vector for the dielectricheating modulator. In this regard, it is known that hypoxic regions arecharacteristic of solid tumors. In particular, certain species ofanaerobic bacteria, including the genera Clostridium andBifidobacterium, can selectively germinate and grow in the hypoxicregions of solid tumors.

As another example, the targeting moiety may comprise a magneticparticle. The dielectric heating modulator associated with the magnetictargeting moiety may be steered to specific locations using magnets ormagnetic resonant imaging (MRI) machines. Thus, when the targetingmoiety comprises a magnetic particle, the dielectric heating modulatorcan be directed toward specific target cells using a magnetic force. Itwill be appreciated that the magnetic force can be either an attractingforce or a repelling force. Further, both the targeting moiety and thedielectric heating modulator may be magnetic. For example, thedielectric heating modulator and targeting moiety may comprise a goldnanoparticle partially or wholly coated with ferrous iron. A magnet maythen be used to localize the coated particle to the biological targets,such as a localized tumor, prior to or during application of thedielectric heating.

It is also contemplated that the dielectric heating modulator may beassociated with multiple targeting moieties. For example, the pluralityof molecular recognition elements can be either similar (e.g.,monoclonal antibodies) or dissimilar (e.g., distinct idiotypes and/orisotypes of antibodies, or an antibody and a nucleic acid, etc).Utilization of more than one targeting moiety allows multiple biologicaltargets to be targeted or to increase affinity for a particularbiological target.

It will be appreciated that in some instances, the dielectric heatingmodulator itself may have targeting attributes. For example, glucose andglucose mimics are preferentially taken up by cancer cells. That is,like a targeting moiety, glucose and glucose mimics selectively targetcancer cells. Such compounds may function as dielectric heatingmodulators, but also have targeting attributes when the biologicaltargets are cancer cells. As another example, a dielectric heatingmodulator may be comprised of a magnetic material, in which case magnetsor MRI machines can be used to steer the magnetic dielectric heatingmodulator toward specific biological targets (e.g., target cells) usingan attracting or repelling magnetic force. In these cases, thedielectric heating modulator does not need to be associated with atargeting moiety (wherein the term “targeting moiety” refers to asubstance, means, or technique that is distinct from the dielectricheating modulator itself).

3. Carrier

The dielectric heating modulator, without or without a targeting moietyassociated therewith, may be administered to the subject in a carrier.Exemplary carriers are described in U.S. Patent Application No.2007/0248537, U.S. Pat. No. 7,329,638, and U.S. Pat. No. 7,5210,555.Carriers are also detailed in Remington's Pharmaceutical Sciences,latest edition, (Mack Publishing). Preferably, the carrier is apharmaceutically acceptable carrier, which is; generally apharmaceutically acceptable material, composition or vehicle, such as aliquid or solid filler, diluent, excipient, solvent or encapsulatingmaterial, involved in carrying or transporting a compound(s) of thepresent invention within or to the subject such that it can, perform itsintended function. Each carrier must be “acceptable” in the sense ofbeing compatible with the other ingredients of the formulation and notinjurious to the subject. In addition, it is preferable that the carriernot substantially interfere with the heating of the dielectric heatingmodulator. The carrier preferably has properties similar to that: of thehuman body. The carrier may be associated with both a dielectric heatingmodulator and a targeting moiety. For example, the targeting moiety maybe attached or otherwise coupled to a liposome, in which the dielectricheating modulator is encapsulated therein.

III. Application of Dielectric Field to Treatment Region of a Subject

As discussed above, the present invention involves placing a treatmentregion of a subject between two electrodes such that the treatmentregion effectively becomes the dielectric of a capacitor. A dielectricfield generated between the electrodes causes polar molecules in thetreatment region to be attracted and repelled by the rapidly changingpolarity of the dielectric field. The friction resulting from thismolecular movement translates into heat throughout the thickness of eachtreatment region in such a manner as to provide substantially evenheating of the treatment region. By contrast, it will be appreciatedthat an electromagnetic field utilizes a standing wave whose amplitudedecreases as it penetrates into a treatment region and, thus, providesuneven heating of the treatment region. Accordingly, the presentinvention relies on the use of a dielectric field for its ability toprovide substantially even heating throughout the thickness of thetreatment region.

Importantly, if a substantially constant current passes between theelectrodes, and through a treatment region, then the same cell typethroughout the treatment region heats at substantially the same rate. Inorder to obtain a substantially constant current, it is also necessaryto obtain a substantially constant voltage between the electrodes.Accordingly, various exemplary embodiments of apparatuses and methodsfor generating a dielectric field between two electrodes in accordancewith the present invention are described below, wherein the voltagebetween the electrodes is substantially constant (as described inSection III.A below) and/or the current passing between the electrodesand through the treatment region is substantially constant (as describedin Section III.B below). Of course, one skilled in the art willunderstand that other apparatuses and methods may also be implemented inaccordance with the present invention.

A. Substantially Constant Voltage

Examples are provided below of apparatuses for generating a dielectricfield between two electrodes wherein the voltage between the electrodesis substantially constant. It should be noted that these examples areprovided to explain the principles that are used to obtain asubstantially constant voltage between the electrodes, which isnecessary to obtain a substantially constant current between theelectrodes and across the treatment region. It will be seen that theexamples provided in Section III.B below (which are the preferredembodiments insofar as a substantially constant current is obtained)rely on the principles discussed herein. Also, as used herein, the term“substantially constant voltage” between electrodes, i.e., a highvoltage electrode and a ground electrode, means that the differencebetween the voltage provided at a point on the high voltage electrodecompared to the voltage provided at each other point on the high voltageelectrode is preferably less than ±10%, more preferably less than ±8%,more preferably less than ±6%, more preferably less than ±4%, and mostpreferably less than ±2%.

Referring to FIG. 1, a diagram of an exemplary apparatus that may beused to generate a dielectric field between two electrodes is designatedas reference numeral 10. Apparatus 10 includes a top electrode 12 and abottom electrode 14 each of which comprises a plate formed of anyconductive material. Top and bottom electrodes 12, 14 are connected toan energy source or generator 16 operable to generate a dielectric fieldbetween the electrodes. In this example, top electrode 12 is the highvoltage electrode while bottom electrode 14 is the ground electrode(although this could be reversed such that the top electrode is theground electrode and the bottom electrode is the high voltageelectrode). The voltage between the electrodes is adjustable and variesbetween different applications. Typically, the voltage between theelectrodes is in the range of 100 volts to 10,000 volts, preferably inthe range of 200 volts to 2,000 volts, and more preferably in the rangeof 300 volts to 500 volts. The dielectric field is generated atfrequencies ranging from about 1 MHz to 100 MHz, and is preferablygenerated at either. 27.12 MHz or 40.68 MHz (both of which are allowedcenter frequencies for industrial, scientific, and medical (ISM)applications). As can be seen, in the illustrated embodiment, thetreatment region comprises the entire human body such that top electrode12 and bottom electrode 14 are positioned proximate to and on eitherside of body and are sized to extend across the surface area of thebody. Of course, the size of the electrodes, will vary depending on thesurface area of the treatment region.

Generator 16 contains a power tube and LC circuit, or may alternativelycontain solid-state technology. Preferably, generator 16 is tuned toresonate at the selected frequency, which occurs when the inductivereactance balances the capacitive reactance at the selected frequency,as follows:

$\begin{matrix}{f = \frac{1}{2\pi \sqrt{LC}}} & (1)\end{matrix}$

where

f=frequency of dielectric field in hertz

L=inductance in henries

C=capacitance in farads.

As shown in FIG. 2, the signal generated by the apparatus of FIG. 1 issubstantially a sinusoid having a wavelength λ. Preferably, thetreatment region is placed between top electrode 12 and bottom electrode14 and generally centered at a position that is ¼λ or, alternatively, ¼λplus a multiple of ½λ (e.g., ¾λ, 1¼, etc.), from the power tube ofgenerator 16. It can be seen that the peak of the sinusoid is located atthese positions, which provides the most constant voltage (i.e., thelowest voltage change) on the sinusoid.

The wavelength of the sinusoid is expressed as follows:

$\begin{matrix}{\lambda = \frac{c}{f}} & (2)\end{matrix}$

where

λ=wavelength of sinusoid in meters

c=speed of light (3×10⁸ m/sec)

f=frequency of dielectric field in hertz.

Using this equation, the wavelength of a sinusoid for a dielectric fieldgenerated at 27.12 MHz is as follows:

$\begin{matrix}{\lambda = {\frac{3 \times 10^{8}}{27.12 \times 10^{6}} = {{11.1\mspace{14mu} {meters}} = {36.3\mspace{20mu} {feet}}}}} & (3)\end{matrix}$

Thus, the ¼λ position is located 9.1 feet from the power tube ofgenerator 16.

Similarly, the wavelength of a sinusoid for a dielectric field generatedat 40.68 MHz is as follows:

$\begin{matrix}{\lambda = {\frac{3 \times 10^{8}}{40.68 \times 10^{6}} = {{7.5\mspace{14mu} {meters}} = {24.6\mspace{14mu} {feet}}}}} & (4)\end{matrix}$

Thus, the ¼λ position is located 6.15 feet from the power tube ofgenerator 16.

One skilled in the art will understand that the use of a lower frequency(e.g., 27.12 MHz) will provide more consistent voltages betweenelectrodes 12 and 14 due to the longer wavelength λ of the generatedsignal. However, the use of a higher frequency (e.g., 40.68 MHz) willheat the treatment region at a faster rate. Thus, for any givenapplication, the desired frequency may be selected with theseconsiderations in mind. Of course, the surface area of the treatmentregion may dictate the desired frequency. For example, if a treatmentregion has a surface area of 18 inches by 24 inches, it is possible touse a higher frequency (e.g., 40.68 MHz). However, if the treatmentregion comprises the entire human body, as in the illustratedembodiment, it would be preferable to use a lower frequency (e.g., 27.12MHz).

As discussed above, apparatus 10 shown in FIG. 1 may be used to applysubstantially constant voltages between electrodes 12 and 14 if thetreatment region is placed at or near the ¼λ position (or,alternatively, ¼λ plus a multiple of ½λ). With this electrodeconfiguration, a single point (designated as point X in FIGS. 1 and 2)is located at the ¼ wavelength position (or, alternatively, ¼λ plus amultiple of ½λ), which corresponds to the highest voltage on thesinusoid. In order to apply even more consistent voltages between theelectrodes, top electrode 12 may be replaced with a top electrode inwhich a plurality of points are located at the ¼ wavelength position(or, alternatively, ¼λ plus a multiple of ½λ), as will be describedbelow.

Referring to FIG. 3, a diagram of an exemplary apparatus that may beused to generate a dielectric field between two electrodes is designatedas reference numeral 20, Apparatus 20 includes a top electrode 22 and abottom electrode 24, both of which are connected to an energy source orgenerator 26 operable to generate a dielectric field between theelectrodes. It should be understood that the only difference betweenapparatus 10 of FIG. 1 and apparatus 20 of FIG. 3 is the configurationof the top electrode. In FIG. 1, top electrode 12 comprises a singleplate. However, in FIG. 3, it can be seen that top electrode 22comprises a plurality of electrically connected plates arranged in atiered configuration. Specifically, top electrode 22 includes a mainplate 22 a located adjacent the treatment region, which is electricallyconnected to plates 22 b, 22 c, 22 d, and 22 e. Then, plates 22 b and 22c are electrically connected to plate 22 f, and plates 22 d and 22 e areelectrically connected to plate 22 g. Further, plates 22 f and 22 g areelectrically connected to plate 22 h, which is electrically connected tothe power tube of the generator (or other solid-state supply). As can beseen, in the illustrated embodiment, the treatment region comprises theentire human body such that, main plate 22 a of top electrode 22 andbottom electrode 24 are positioned proximate to and on either side ofthe human body and are sized to extend across the surface area of thehuman body. Of course, the size of the electrodes will vary depending onthe surface area of the treatment region.

As shown in FIG. 3, points A, B, C, D, E, F, G, and H are evenly spacedalong the length of main plate 22 a, and the power tube of the generatoris designated as point O. The size and positioning of the various platesare chosen such that the distances OA, OB, OC, OD, OE, OF, OG, and OHare the same and, thus, points A, B, C, D, E, F, G, and H are eachlocated at the ¼ wavelength position (or, alternatively, ¼λ plus amultiple of ½λ). For example, if the selected frequency is 27.12 MHz or40.68 MHz, each of points A, B, C, D; E, F, G, and H would be located9.1 feet or 6.15 feet, respectively, from point O. By contrast, as shownin FIG. 1, only point X is located at the ¼ wavelength position.

FIG. 4 shows the peak of the signal generated by the apparatus of FIG.3, wherein points A, B, C, D, E, F, G, and H are located at the ¼wavelength position (or, alternatively, ¼λ plus a multiple of ½λ). Thepeak of the sinusoid of FIG. 2, along with point X, is superimposedthereon in order to illustrate the differences between theconfigurations of top electrode 12 (FIG. 1) and top electrode 22 (FIG.3). As can be seen, point X and points A, B, C, D, E, F, G, and H areeach located at the peak of the sinusoid, which corresponds to thehighest voltage. In effect, the configuration of top electrode 22substantially flattens-out the peak of the sinusoid. As such, topelectrode 22 may be used to apply more consistent voltages betweenelectrodes 22 and 24 as compared to top electrode 12.

Of course, one skilled in the art will understand that top electrode 22is merely an example of an electrode that may be used to provide moreconsistent voltages between the electrodes. Other configurations mayalso be used in which multiple points (i.e., more or fewer points thanthe eight points shown in FIG. 3) are located at the ¼ wavelengthposition (or, alternatively, ¼λ plus a multiple of ½λ). Stated anotherway, the top electrode may comprise any configuration of electricallyconnected plates that are sized and positioned such that each of aplurality of points are located the same distance from the power tube ofthe generator.

B. Substantially Constant Current

The current of a dielectric field is dependent in part on the dielectricconstant of the materials placed between the electrodes, wherein thedielectric constant determines how much current goes through a materialfor an applied voltage. Specifically, if a material with a lowdielectric constant is placed between the electrodes, the currentpassing through the material will be relatively low. By contrast, if amaterial with a high dielectric constant is placed between theelectrodes, the current passing through the material will be relativelyhigh.

In the case of a human body, the material between the electrodes variesbetween different regions of the body due to the irregular shape of thebody. For example, the chest region may be about 8 inches thick and theshoulder region may be about 4 inches thick. As such, if the human bodyis placed in apparatus 10 of FIG. 1 or apparatus 20 of FIG. 3 and theelectrodes are spaced 8 inches apart, the material between theelectrodes in the chest region is the human body (i.e., the 8 inchthickness of the chest region) and the material between the electrodesin the shoulder region is a combination of the human body and air (i.e.,the 4 inch thickness of the shoulder region and 4 inches of air). Forexemplary purposes, assume that the dielectric constant of the humanbody is approximately 71 (the dielectric constant actually varies basedon the cell type, as discussed more fully below), which is markedlyhigher than the dielectric constant of air, which is approximately 1.Because of the differences between the dielectric constants, the currentin the chest region will be significantly higher than the current in theshoulder region. As such, the chest region will heat at a significantlyfaster rate than the shoulder region.

In order to alleviate this problem, any air between a treatment regionand the electrodes is preferably displaced with one or more flowablematerials having a dielectric constant and dissipation factor that allowa substantially constant current to be applied across the treatmentregion. As used herein, the term “substantially constant current” meansthat the difference between the current passing through a portion of atreatment region compared to the current passing through each otherportion of the treatment region, is preferably less than ±25%, morepreferably less than ±20%, more preferably less than ±15%, more:preferably less than ±10%, and most preferably less than ±5%. Theselection of a flowable material is virtually non-limiting and maycomprise a liquid, gel, paste, putty, slurry, suspension, or otherflowable material. Preferably, each flowable material has a relativelylow dissipation factor so that the increase in temperature of theflowable material is minimal at the end of the dielectric heatingtreatment. A suitable flowable material is distilled water, which has adielectric constant of 76 and a dissipation factor of 0.005, which isoptionally mixed with a suitable additive to modify the overalldielectric constant of the flowable material. Each flowable materialpreferably has a viscosity that allows the material to conform to thecontours of the body. For example, materials having a viscosity of 1,10, 100, 10,000, 100,000, or even 1,000,000 cps may be used.

As just discussed, in one aspect, a flowable material comprisesdistilled water mixed with an additive, which is preferably miscible inwater. Examples of suitable additives are carboxylic acids, esters,ketones, alcohols, amines, and the like. Preferred additives include,but are not limited to, C1 to C6 branched or straight chain carboxylicacids (e.g., acetic acid), C1 to C6 alcohols and polyols (e.g.,polyalkylene glycols, methanol, ethanol, n-propanol, isopropanol,butanol, isobutyl ethanol, hexylene glycol), C1 to C6 ketones (e.g.,acetone, methyl isobutyl ketone), and C1 to C6 esters (e.g., butylacetate). As other examples, the additive may comprise a salt, such asmagnesium chloride, sodium chloride, or potassium chloride. Exemplaryamines are cyclic amines, such as 1,8-Diazabicyclo[5.4.0]undec-7-ene(“DBU”). In general, the additive may comprise any compound in which thedissipation factor is relatively low so that the increase in temperatureof the flowable material is minimal at the end of the dielectric heatingtreatment, and, in which the dielectric constant is chosen to allow asubstantially constant current to be applied across the treatment region(i.e., a relatively low dielectric constant will decrease the currentand a relatively high dielectric constant will increase the current).

The types of apparatuses and methodologies that may be used to apply adielectric field having a substantially constant current across atreatment region will vary depending on the amount of adipose tissue(referred to herein as “fat”) located within the treatment region inview of the fact that fat heats at a substantially faster rate thanother cell types in the body. Examples are provided below for cases inwhich (1) the treatment region contains a substantially constant amountof fat (Example 1 below) and (2) the treatment region does not contain asubstantially constant amount of fat, i.e., different sub-regionscontain different amounts of fat (Examples 2 and 3 below). As usedherein, the term “substantially constant amount of fat” means that thedifference between the amount of fat in a cross-sectional area of atreatment region or sub-region compared to the amount of fat in eachother cross-sectional area of the treatment region or sub-region ispreferably less than ±5%, more preferably less than ±4%, more preferablyless than ±3%, more preferably less than ±2%, and most preferably lessthan ±1%. It should be understood that a treatment region or sub-regionmay contain a substantially constant amount of fat even if the treatmentregion or sub-region is substantially fat-free. As used herein, the term“substantially fat-free” means that a treatment region or sub-regioncontains an amount of fat that is preferably less than 15% of the volumeof the treatment region or sub-region, more preferably less than 10% ofthe volume of the treatment region or sub-region, and most preferablyless than 5% of the volume of the treatment region or sub-region.

As will be apparent from the description below, the appropriatemethodology will depend on the amount of fat located within thetreatment region and sub-regions of the body. Of course, one skilled inthe art will understand that the apparatuses and methodologies describedbelow are merely examples that can be used to obtain a substantiallyconstant current across the treatment region, and that other apparatusesand methodologies may be used in accordance with the present invention.

1. Treatment Region Contains a Substantially Constant Amount of Fat

a. Exemplary Apparatuses

Referring to FIG. 5, a diagram of an exemplary apparatus that may beused to generate a dielectric field between two electrodes and across atreatment region that contains a substantially constant amount of fat isdesignated as reference numeral 30. Apparatus 30 includes a topelectrode 32 and a bottom electrode 34, both of which are connected toan energy source or generator 36 operable to generate a dielectric fieldbetween the electrodes. Preferably, the voltage between top electrode 32and bottom electrode. 34 is substantially constant, which isaccomplished by centering the treatment region at a position that is ¼λor, alternatively, ¼λ plus a multiple of ½λ, from the power tube ofgenerator 36 (as discussed above in connection with FIG. 1) or providingmultiple points at this position (as discussed above in connection withFIG. 3). As can be seen, top electrode 32 comprises a plate and bottomelectrode 34 has a generally U-shaped configuration so as to define abath cavity 34 a therein;

Referring still to FIG. 5, the treatment region in the illustratedembodiment comprises a human body that contains a substantially constantamount of fat. The body is placed within bath cavity 34 a, and aflowable material is disposed therein so as to displace the air betweenthe body and electrodes. In accordance with the present invention, theflowable material has a dielectric constant and dissipation factor thatallows a substantially constant current to be obtained across the body.Of course, apparatus 30 may be configured such that the head or anyother region of the body is positioned outside of bath cavity 34 a so asnot to form a part of the treatment region. One skilled in the art willappreciate that apparatus 30 may have a variety of different structuralconfigurations that are encompassed by the present invention.

Referring to FIGS. 6 a and 6 b, a diagram of an exemplary apparatus thatmay be used to generate a dielectric field between two electrodes andacross a treatment region that contains a substantially constant amountof fat is designated as reference numeral 40. Apparatus includes a topelectrode 42 and a bottom electrode 44, both of which are connected toan energy source or generator 46 operable to generate a dielectric fieldbetween the electrodes. Preferably, the voltage between top electrode 42and bottom electrode. 44 is substantially constant, which isaccomplished by centering the treatment region at a position that is ¼λor, alternatively, ¼λ plus a multiple of ¼λ, from the power tube ofgenerator 46 (as discussed above in connection with FIG. 1) or providingmultiple points at this position (as discussed above in connection withFIG. 3). As can be seen, top electrode 42 and bottom electrode 44 eachcomprise a plate, and disposed between the electrodes is a top bladder48 (attached to top electrode 42) and a bottom bladder 50 (attached tobottom electrode 44). Top and bottom bladders 48, 50 may be made of anyflexible and stretchable material, such as silicone rubber or liquidsilicone rubber sold by Rhodia Silicones, so that the bladders are ableto stretch when filled with a flowable material. Top and bottom bladders48, 50 are continuous in the sense that a single top bladder extendsacross the surface area of top electrode 42 and a single bottom bladderextends across the surface area of bottom electrode 44 so as to define acavity therebetween.

As shown in FIG. 6 b, the treatment region in the illustrated embodimentcomprises a human body that contains a substantially constant amount offat. The body is placed within the cavity between top and bottombladders 48, 50, and a flowable material is injected into each of topand bottom bladders 48, 50 so as to displace the air between the bodyand electrodes. As such, the top of the body is in contact with topbladder 48 and the bottom of the body is in contact with bottom bladder50. In accordance with the present invention, the flowable materialinjected into top and bottom bladders 48, 50 has a dielectric constantand dissipation factor that allows a substantially constant current tobe obtained across the body. Preferably, the same flowable material isinjected into top and bottom bladders 48, 50, although the use ofdifferent flowable materials is also contemplated. One skilled in theart will appreciate that apparatus 40 may have a variety of differentstructural configurations that are encompassed by the present invention.It should also be understood that the treatment region need not comprisethe entire human body, and that only a portion of a body may bepositioned between the electrodes of apparatus 40.

b. General Methodology I

For cases in which a treatment region of a body contains a substantiallyconstant amount of fat, the treatment region is placed in apparatus 30shown in FIG. 5, and a flowable material is disposed within bath cavity34 a so as to displace the air between the treatment region andelectrodes. Alternatively, the treatment region is placed in apparatus40 shown in FIG. 6 a, and a flowable material is injected into topbladder 48 and bottom bladder 50. In either case, the composition of theflowable material is chosen so as to obtain a substantially constantcurrent across the treatment region so that the same cell type indifferent sub-regions of the treatment region heats at substantially thesame rate. This is accomplished by utilizing a flowable material that“simulates the body.” as discussed below.

In one aspect, the flowable material simulates the body if it has adissipation factor and dielectric constant that are substantially thesame as the body. For example, if the body is a human body and thedielectric field has a frequency of 40 MHz, the flowable materialpreferably has a dissipation factor of about 1.8 and a dielectricconstant of about 71 (i.e., the dissipation factor and dielectricconstant of many cell types in the human body). In this case, thecurrent passing through the treatment region is the same regardless ofthe different thickness sections of the treatment region. Because theflowable material will heat at substantially the same rate as thetreatment region, it is preferable to chill the flowable material priorto, during and/or after the dielectric heating treatment so as toprovide a cooling effect on the skin of the body.

In another aspect, the flowable material has a dissipation factor anddielectric constant that are different than those of the body; however,the relationship between the dissipation factor and dielectric constantare such that the flowable material simulates the body. Preferably, theflowable material has a lower dissipation factor than the body so thatthe flowable material heats at a slower rate than the body. As such, theflowable material has a dissipation factor that is preferably less than1.0, more preferably less than 0.5, and most preferably less than 0.3.In this case, the required values of the dissipation factor anddielectric constant of the flowable material are calculated so as toobtain a substantially constant current across the treatment region and,then, such values are used to determine the composition of the flowablematerial. For example, it will be seen in Example 1 below that anacceptable flowable material is comprised of a mixture of 83.42%distilled water and 16.58% acetic acid, which has a dissipation factorof 0.02003 and a dielectric constant of 26.5. With this flowablematerial, there is a minor difference between the current passingthrough the different, thickness sections of the treatment region.However, the current difference is small and nonetheless results in theapplication of a substantially constant current across the treatmentregion.

Example 1

An example using this general methodology is provided below in which ahuman body is placed in apparatus 40 shown in FIG. 6 a, wherein thetreatment region includes the chest and shoulder regions of the body.The chest region has a thickness of 8 inches and the shoulder region hasa thickness of 4 inches. In this example, it is assumed that the chestand, shoulder regions of the body are substantially fat-free. The topand bottom electrodes 42 and 44 are spaced 8 inches apart, and thevoltage between the electrodes is 1,000 volts. A flowable materialcomprising distilled water mixed with acetic acid (in volumes to becalculated below) is injected into top bladder 48 and bottom bladder 50.Accordingly, the material between the electrodes in the chest region isthe human body (i.e., the 8 inch chest region abuts against bothelectrodes) and the material between the electrodes in the shoulderregion is the human body and the distilled water/acetic acid mixture(i.e., the 4 inch shoulder region and 4 inches of the distilledwater/acetic acid mixture).

The following table identifies the dielectric constant, dissipationfactor, specific heat and density of each of the materials between theelectrodes, assuming that the frequency of the dielectric field is 40MHz:

Dielectric Dissipation Specific Heat Density Constant Factor (J/g ° C.)(g/cm³) Human Body 71 1.8 3.47 1.027 (Chest and Shoulder Regions)Distilled 76 0.005 4.18 1 Water Acetic Acid 6.20 0.0262 2.18 1.05

In order to obtain a substantially constant current across the chest andshoulder regions of the body so that the same cell type in both regionsheats at substantially the same rate, the current passing through theshoulder region and surrounding distilled water/acetic acid mixture mustbe substantially the same as the current passing through the chestregion. The following calculations are performed to determine the volumeof distilled water and the volume of acetic acid that will result in asubstantially constant current across the chest and shoulder regions ofthe body. In the following equations, the subscript 1 denotes the chestregion of the body, the subscript 2 denotes the shoulder region of thebody, and the subscript 3 denotes the distilled water/acetic acidmixture (wherein the subscript dw denotes the distilled water and thesubscript aa denotes the acetic acid in certain equations).

Calculations for Chest Region

The capacitance of the chest region is expressed by the followingequation:

$\begin{matrix}{C_{1} = \frac{ɛ_{1} \times ɛ_{0} \times A}{d_{1}}} & (5)\end{matrix}$

where

C₁=capacitance of chest region in farads

∈₁=dielectric constant of chest region

∈₀=electric constant (8.854×10⁻¹² farad/meter)

A=area of chest region in meters²

d₁=thickness of chest region in meters.

Equation (5) may be simplified and rewritten so that the thickness ofthe chest region is expressed in inches (noting that 1 meter=39.37inches), as follows:

$\begin{matrix}{C_{1} = \frac{ɛ_{1} \times A \times 0.2249}{d_{1}}} & (6)\end{matrix}$

where

C₁=capacitance of chest region in picofarads

∈₁=dielectric constant of chest region

A=area of chest region in inches²

d₁=thickness of chest region in inches.

It should be noted that equation (6) (rather than equation (5)) will beused throughout the specification to refer to the capacitance of atreatment region, sub-region or other material.

Assuming that the dielectric constant of the chest region is 71 and thatthe unit area is 1 inch², the capacitance of the chest region is:

$\begin{matrix}{C_{1} = {\frac{71 \times 1 \times 0.2249}{8} = {1.9932\mspace{14mu} {pF}}}} & (7)\end{matrix}$

The capacitive reactance of the chest region is given by the followingequation:

$\begin{matrix}{X_{C\; 1} = \frac{1}{2 \times \pi \times f \times C_{1}}} & (8)\end{matrix}$

where

X_(C1)=capacitive reactance of chest region in ohms

f=frequency of dielectric field in hertz

C₁=capacitance of chest region in farads.

Using the capacitance of the chest region derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the chest region is:

$\begin{matrix}{X_{C\; 1} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 1.9932 \times 10^{- 12}} = {1\text{,}996.2\mspace{14mu} {ohms}}}} & (9)\end{matrix}$

The resistance of the chest region is equal to the product of thedissipation factor of the chest region and the capacitive reactance ofthe chest region, as follows:

R ₁ =df ₁ ×X _(C1)  (10)

where

R₁=resistance of chest region in ohms

df₁=dissipation factor of chest region

X_(c1)=capacitive reactance of chest region in ohms.

Using the capacitive reactance of the chest region derived above andassuming that the dissipation factor of the chest region is 1.8, theresistance of the chest region is expressed as follows:

R ₁=1.8×1,996.2=3,593.2 ohms  (11)

Next, the current passing between the electrodes through the chestregion is represented by the following equation:

$\begin{matrix}{I = \frac{V}{\sqrt{X_{C\; 1}^{2} + R_{1}^{2}}}} & (12)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C1)=capacitive reactance of chest region in ohms

R₁=resistance of chest region in ohms.

Using the capacitive reactance and resistance of the chest regionderived above and assuming that the voltage between the electrodes is1,000 volts, the current passing between the electrodes through thechest region is:

$\begin{matrix}{I = {\frac{1,000}{\sqrt{{1,996.2^{2}} + {3,593.2^{2}}}} = {0.24328\mspace{14mu} {amps}}}} & (13)\end{matrix}$

The power that is dissipated in the chest region due to the applicationof the dielectric field (over an area of 1 inch²) is expressed by thefollowing equation:

P ₁ =R ₁ ×I ²  (14)

where

P₁=power in chest region in watts due to the dielectric field (over anarea of 1 inch²)

R₁=resistance of chest region in ohms

I=current in amperes.

Using the resistance of the chest region and the current derived above,the power dissipated in the chest region due to the dielectric field(over an area of 1-inch²) is:

P ₁=3,593.2×(0.24328)²=212.67 watts  (15)

The increase in temperature of the chest region during the applicationof the dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{1}} = \frac{P_{1} \times t_{1}}{h_{1} \times \rho_{1} \times d_{1}}} & (16)\end{matrix}$

where

ΔT₁=increase in temperature of chest region in ° C.

P₁=power in chest region in watts due to the dielectric field (over anarea of 1 inch²)

t₁=heating time of chest region in seconds

h₁=specific heat of chest region in J/g ° C.

ρ₁=density of chest region in g/inches³

d₁=thickness of chest region in inches.

Equation (16) may be rewritten so that the density of the chest regionis expressed in g/cm³ (noting that 1 inch=2.54 cm), as follows:

$\begin{matrix}{{\Delta \; T_{1}} = \frac{P_{1} \times t_{1}}{16.387 \times h_{1} \times \rho_{1} \times d_{1}}} & (17)\end{matrix}$

where

ΔT₁=increase in temperature of chest region in ° C.

P₁=power in chest region in watts due to, the dielectric field (over anarea of 1 inch²)

t₁=heating time of chest region in seconds

h₁=specific heat of chest region in J/g ° C.

ρ₁=density of chest region in g/cm³

d₁=thickness of chest region in inches.

It should be noted that equation (17) (rather than equation (16)) willbe used throughout the specification to refer to the increase intemperature of a treatment region, sub-region or other material.

Using the power in the chest region derived above and assuming that thespecific heat and density of the chest region are 3.47 J/g ° C. and1.027 g/cm³, respectively, the increase in temperature of the chestregion during the application of the dielectric field is expressed asfollows:

$\begin{matrix}{{\Delta \; T_{1}} = {\frac{212.67 \times t_{1}}{16.387 \times 3.47 \times 1.027 \times 8} = {0.4552 \times t_{1}{^\circ}\mspace{14mu} {C.}}}} & (18)\end{matrix}$

Calculations for Shoulder Region and Distilled Water/Acetic Acid Mixture

The capacitance of the shoulder region is expressed by the followingequation:

$\begin{matrix}{C_{2} = \frac{ɛ_{2} \times A \times 0.2249}{d_{2}}} & (19)\end{matrix}$

where

C₂=capacitance of shoulder region in picofarads

∈₂=dielectric constant of shoulder region

A=area of shoulder region in inches²

d₂=thickness of shoulder region in inches.

Assuming that the dielectric constant of the shoulder region is 71 andthat the unit area is 1 inch², the capacitance of the shoulder regionis:

$\begin{matrix}{C_{2} = {\frac{71 \times 1 \times 0.2249}{4} = {3.9864\mspace{14mu} {pF}}}} & (20)\end{matrix}$

The capacitive reactance of the shoulder region is then given by thefollowing equation:

$\begin{matrix}{X_{C\; 2} = \frac{1}{2 \times \pi \times f \times C_{2}}} & (21)\end{matrix}$

where

X_(C2)=capacitive reactance of shoulder region in ohms

f=frequency of dielectric field in hertz

C₂=capacitance of shoulder region in farads.

Using the capacitance of the shoulder region derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the shoulder region is:

$\begin{matrix}{X_{C\; 2} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 3.9864 \times 10^{- 12}} = {998.112\mspace{14mu} {ohms}}}} & (22)\end{matrix}$

The resistance of the shoulder region is equal to the product of thedissipation factor of the shoulder region and the capacitive reactanceof the shoulder region, as follows:

R ₂ =df ₂ ×X _(C2)  (23)

where

R₂—resistance of shoulder region in ohms

df₂=dissipation factor of shoulder region

X_(C2)=capacitive reactance of shoulder region in ohms.

Using the capacitive reactance of the shoulder region derived above andassuming that the dissipation factor of the shoulder region is 1.8, theresistance of the shoulder region is expressed as follows:

R ₂=1.8×998.112=1,796.6 ohms  (24)

The increase in temperature of the shoulder region during theapplication of the dielectric field is represented by the followingequation:

$\begin{matrix}{{\Delta \; T_{2}} = \frac{P_{2} \times t_{2}}{16.387 \times h_{2} \times \rho_{2} \times d_{2}}} & (25)\end{matrix}$

where

ΔT₂=increase in temperature of shoulder region in ° C.

P₂=power in shoulder region in watts due to the dielectric field

t₂=heating time of shoulder region in seconds

h₂=specific heat of shoulder region in J/g ° C.

ρ₂=density of shoulder region in g/cm³

d₂=thickness of shoulder region in inches.

Assuming that the specific heat and density of the shoulder region are3.47 J/g° C. and 1.027 g/cm³, respectively, the increase in temperatureof the shoulder region during the application of the dielectric field isexpressed as follows:

$\begin{matrix}{{\Delta \; T_{2}} = {\frac{P_{2} \times t_{2}}{16.387 \times 3.47 \times 1.027 \times 4} = {0.00428 \times P_{2} \times t_{2}{^\circ}\mspace{14mu} {C.}}}} & (26)\end{matrix}$

In order for the shoulder region to heat at the same rate as the chestregion, the increase in temperature of the shoulder region (ΔT₂) must beequal to the increase in temperature of the chest region (ΔT₁), and, theheating time of the shoulder region (t₂) must be equal to the heatingtime of the chest region (t₁). In this case, equations (18) and (26) maybe combined and simplified as follows:

$\begin{matrix}{P_{2} = {\frac{0.4552`}{0.00428} = {106.335\mspace{14mu} {watts}}}} & (27)\end{matrix}$

The power that is dissipated in the shoulder region due to theapplication of the dielectric field is expressed by the followingequation:

P ₂ =R ₂ ×I ²  (28)

where

P₂=power in shoulder region in watts due to the dielectric field

R₂=resistance of shoulder region in ohms

I=current in amperes.

Using the power dissipated in the shoulder region and the resistance ofthe shoulder region derived above, the power dissipated in the shoulderregion due to the dielectric field is expressed as:

106.335=1,796.6×I ²  (29)

By solving equation (29) for I, it can be seen that the current passingbetween the electrodes through the shoulder region is:

$\begin{matrix}{I = {\sqrt{\frac{106.335}{1,796.6}} = {0.24328\mspace{14mu} {amps}}}} & (30)\end{matrix}$

Thus, the current passing between the electrodes through the shoulderregion (see equation (30)) is equal to the current passing between theelectrodes through the chest region (see equation (13)).

Now, the capacitance of the distilled water/acetic acid mixture adjacentthe shoulder region is expressed by the following equation:

$\begin{matrix}{C_{3} = \frac{ɛ_{3} \times A \times 0.2249}{d_{3}}} & (31)\end{matrix}$

where

C₃=capacitance of mixture in picofarads

∈₃=dielectric constant of mixture

A=area of mixture in inches²

d₃=thickness of mixture in inches.

For a unit area of 1 inch², the capacitance of the distilledwater/acetic acid mixture is:

$\begin{matrix}{C_{3} = {\frac{ɛ_{3} \times 1 \times 0.2249}{4} = {ɛ_{3} \times 0.05617\mspace{14mu} {pF}}}} & (32)\end{matrix}$

The capacitive reactance of the distilled water/acetic acid mixture isthen given by the following equation:

$\begin{matrix}{X_{C\; 3} = \frac{1}{2 \times \pi \times f \times C_{3}}} & (33)\end{matrix}$

where

X_(C3)=capacitive reactance of mixture in ohms

f=frequency of dielectric field in hertz

C₃=capacitance of mixture in farads.

Using the capacitance of the distilled water/acetic acid mixture derivedabove and assuming that the frequency of the dielectric field is 40 MHz,the capacitive reactance of the distilled water/acetic acid mixture is:

$\begin{matrix}{X_{C\; 3} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times ɛ_{3} \times 0.05617 \times 10^{- 12}} = {\frac{70,836}{ɛ_{3}}\mspace{14mu} {ohms}}}} & (34)\end{matrix}$

The resistance of the distilled water/acetic acid mixture is equal tothe product of the dissipation factor of the distilled water/acetic acidmixture and the capacitive reactance of the distilled water/acetic acidmixture, as follows:

R ₃ =df ₃ ×X _(C3)  (35)

where

R₃=resistance of mixture in ohms

df₃=dissipation factor of mixture

X_(C3)=capacitive reactance of mixture in ohms.

Using the capacitive reactance of the distilled water/acetic acidmixture-derived above, the resistance of the distilled water/acetic acidmixture is:

$\begin{matrix}{R_{3} = {{df}_{3} \times \frac{70,836}{ɛ_{3}}\mspace{14mu} {ohms}}} & (36)\end{matrix}$

Next, the current passing between the electrodes through the distilledwater/acetic acid mixture and shoulder region is represented by thefollowing equation:

$\begin{matrix}{I = \frac{V}{\sqrt{\left( {X_{C\; 2} + X_{C\; 3}} \right)^{2} + \left( {R_{2} + R_{3}} \right)^{2}}}} & (37)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C2)=capacitive reactance of shoulder region in ohms

X_(C3)=capacitive reactance of mixture in ohms

R₂=resistance of shoulder region in ohms

R₃=resistance of mixture in ohms.

Using the current passing between the electrodes through the shoulderregion derived above (which is the same as the current passing throughthe distilled water/acetic acid mixture and shoulder region), using thecapacitive reactance and resistance of each of the shoulder region anddistilled water/acetic acid mixture derived above, and assuming that thevoltage between the electrodes is 1,000 volts, the current passingbetween the electrodes through the distilled water/acetic acid mixtureand shoulder region is:

$\begin{matrix}{0.24328 = {\frac{1,000}{\sqrt{\left( {998.112 + \frac{70,836}{ɛ_{3}}} \right)^{2} + \left( {{1,796.6} + \frac{{df}_{3} \times 70,836}{ɛ_{3}}} \right)^{2}}}\mspace{14mu} {amps}}} & (38)\end{matrix}$

Now, assume that the distilled water/acetic acid mixture consists of avolume of distilled water represented by x and a volume of acetic acidrepresented by 1−x. It is desired to find the value of x such that thedielectric constant of the distilled water/acetic acid mixture (∈₃) andthe dissipation factor of the distilled water/acetic acid mixture (df₃)satisfy equation (38).

The capacitance of the distilled water is expressed by the followingequation:

$\begin{matrix}{C_{dw} = \frac{ɛ_{dw} \times A \times 0.2249}{d_{dw}}} & (39)\end{matrix}$

where

C_(dw)=capacitance of distilled water in picofarads

∈_(dw)=dielectric constant of distilled water

A=area of distilled water in inches²

d_(dw)=thickness of distilled water in inches.

For a unit area of 1 inch², the capacitance of the distilled water is:

$\begin{matrix}{C_{dw} = {\frac{76 \times 1 \times 0.2249}{4x} = {\frac{4.267}{x}\mspace{14mu} {pF}}}} & (40)\end{matrix}$

Similarly, the capacitance of the acetic acid is expressed by thefollowing equation:

$\begin{matrix}{C_{aa} = \frac{ɛ_{aa} \times A \times 0.2249}{d_{aa}}} & (41)\end{matrix}$

where

C_(aa)=capacitance of acetic acid in picofarads

∈_(aa)=dielectric constant of acetic acid

A=area of acetic acid in inches²

d_(aa)=thickness of acetic acid in inches.

For a unit area of 1 inch², the capacitance of the acetic acid is:

$\begin{matrix}{C_{aa} = {\frac{6.2 \times 1 \times 0.224}{4\left( {1 - x} \right)} = {\frac{0.3481}{1 - x}\mspace{14mu} {pF}}}} & (42)\end{matrix}$

The capacitive reactance of the distilled water is then given by thefollowing equation:

$\begin{matrix}{X_{Cdw} = \frac{1}{2 \times \pi \times f \times C_{dw}}} & (43)\end{matrix}$

where

X_(Cdw)=capacitive reactance of distilled water in ohms

f=frequency of dielectric field in hertz

C_(dw)=capacitance of distilled water in farads.

Using the capacitance of the distilled water derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the distilled water is:

$\begin{matrix}{X_{Cdw} = {\frac{x}{2 \times \pi \times 40 \times 10^{6} \times 4.267 \times 10^{- 12}} = {932.47x\mspace{14mu} {ohms}}}} & (44)\end{matrix}$

Similarly, the capacitive reactance of the acetic acid is given by thefollowing equation:

$\begin{matrix}{X_{Caa} = \frac{1}{2 \times \pi \times f \times C_{aa}}} & (45)\end{matrix}$

where

X_(Caa)=capacitive reactance of acetic acid in ohms

f=frequency of dielectric field in hertz

C_(aa)=capacitance of acetic acid in farads.

Using the capacitance of the acetic acid derived above and assuming thatthe frequency of the dielectric field is 40 MHz; the capacitivereactance of the acetic acid is:

$\begin{matrix}{X_{Caa} = {\frac{1 - x}{2 \times \pi \times 40 \times 10^{6} \times 0.3481 \times 10^{- 12}} = {11,430.26\left( {1 - x} \right)\mspace{14mu} {ohms}}}} & (46)\end{matrix}$

Now, the total capacitive reactance of the distilled water/acetic acidmixture is expressed as follows:

X _(C3) =X _(Cdw) +X _(Caa)  (47)

where

X_(C3)=capacitive reactance of mixture in ohms

X_(Cdw)=capacitive reactance of distilled water in ohms

X_(Caa)=capacitive reactance of acetic acid in ohms.

Using the capacitive reactance of each of the distilled water and aceticacid derived above, the capacitive reactance of the distilledwater/acetic acid mixture is:

X _(C3)=(932.47x)+(11,430.26(1−x))=11,430.26−10,497.8x ohms  (48)

The resistance of the distilled water is equal to the product of thedissipation factor of the distilled water and the capacitive reactanceof the distilled water, as follows:

R _(dw) =df _(dw) ×X _(Cdw)  (49)

where

R_(dw)=resistance of distilled water in ohms

df_(dw)=dissipation factor of distilled water

X_(Cdw)=capacitive reactance of distilled water in ohms.

Using the capacitive reactance of the distilled water derived above, andassuming that the dissipation factor of distilled water is 0.005, theresistance of the distilled water is:

R _(dw)=0.005×932.47x=4.66x ohms  (50)

Similarly, the resistance of the acetic acid is equal to the product ofthe dissipation factor of the acetic acid and the capacitive reactanceof the acetic acid, as follows:

R _(aa) =df _(aa) ×X _(Caa)  (51)

where

R_(aa)=resistance of acetic acid in ohms

df_(aa)=dissipation factor of acetic acid

X_(Caa)=capacitive reactance of acetic acid in ohms.

Using the capacitive reactance of the acetic acid derived above andassuming that the dissipation factor of acetic acid is 0.0262, theresistance of the acetic acid is:

R _(aa)=0.0262×11,430.26(1−x)=299.47(1−x) ohms  (52)

Now, the total resistance of the distilled water/acetic acid mixture isexpressed as follows:

R ₃ =R _(dw) +R _(aa)  (53)

where

R₃=resistance of mixture in ohms

R_(dw)=resistance of distilled water in ohms

R_(aa)=resistance of acetic acid in ohms.

Using the resistance of each of the distilled water and acetic acidderived above, the resistance of the distilled water/acetic acid mixtureis:

R ₃=(4.66x)+(299.47(1−x))=299.47−294.81x ohms  (54)

Next, the current passing between the electrodes through the distilledwater/acetic acid mixture and shoulder region may be represented by thefollowing equation:

$\begin{matrix}{I = \frac{V}{\sqrt{\left( {X_{C\; 2} + X_{C\; 3}} \right)^{2} + \left( {R_{2} + R_{3}} \right)^{2}}}} & (55)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C2)=capacitive reactance of shoulder region in ohms

X_(C3)=capacitive reactance of mixture in ohms

R₂=resistance of shoulder region in ohms

R₃=resistance of mixture in ohms.

Using the current passing between the electrodes through the distilledwater/acetic acid mixture and shoulder region derived above, using thecapacitive reactance and resistance of the distilled water/acetic acidmixture derived above, and assuming that the voltage between theelectrodes is 1,000 volts, the current passing between the electrodesthrough the distilled water/acetic acid mixture and shoulder region is:

$\begin{matrix}{0.24328 = {\frac{1,000}{\sqrt{\left( {{12,428.372} - {10,497.79x}} \right)^{2} + \left( {{2,096.07} - {294.81x}} \right)^{2}}}\mspace{14mu} {amps}}} & (56)\end{matrix}$

By solving equation (56) for x, it can be seen that the volume ofdistilled water represented by x is 0.8342 and, thus, the volume ofacetic acid represented by (1−x) is 0.1658. In other words, thedistilled water/acetic acid mixture is 83.42% distilled water (byvolume); and 16.58% acetic acid (by volume).

By combining equations (34) and (48) (with x=0.8342), the capacitivereactance of the distilled water/acetic acid mixture is:

$\begin{matrix}{X_{C\; 3} = {\frac{70,836}{ɛ_{3}} = {{11,430.26} - {\left( {10,497.8 \times 0.8342} \right)\mspace{14mu} {ohms}}}}} & (57)\end{matrix}$

By solving equation (57) for ∈₃, it can be seen that the dielectricconstant of the distilled water/acetic acid mixture is 26.5.

The dissipation factor of the distilled water/acetic acid mixture isequal to the resistance of the distilled water/acetic acid mixturedivided by the capacitive reactance of the distilled water/acetic acidmixture, as follows:

$\begin{matrix}{{df}_{3} = \frac{R_{3}}{X_{3}}} & (58)\end{matrix}$

where

df₃=dissipation factor of mixture

R₃=resistance of mixture in ohms

X_(C3)=capacitive reactance of mixture in ohms.

Using the resistance and capacitive reactance of the distilledwater/acetic acid mixture derived above (with x=0.8342), the dissipationfactor of the distilled water/acetic acid mixture is:

$\begin{matrix}{{df}_{3} = {\frac{299.47 - \left( {294.81 \times 0.8342} \right)}{2\text{,}673} = 0.02003}} & (59)\end{matrix}$

The power that is dissipated in the distilled water/acetic acid mixturedue to the application of the dielectric field is expressed by thefollowing equation:

P ₃ =R ₃ ×I ²  (60)

where

P₃=power in mixture in watts due to the dielectric field

R₃=resistance of mixture in ohms

I=current in amperes.

Using the resistance of the distilled water/acetic acid mixture and thecurrent derived above, the power dissipated in the distilledwater/acetic acid mixture due to the dielectric field is:

P ₃=(299.47−(294.81×0.8342))×(0.24328)²=3.166 watts  (61)

It can be appreciated that the power dissipated in the distilledwater/acetic acid mixture due to the dielectric field (i.e., 3.166watts) is relatively small in comparison to the power dissipated in thechest region (i.e., 212.67 watts) and the shoulder region (i.e., 106.335watts). Thus, in this example, the power “lost” due to the distilledwater/acetic acid mixture is less than 1% of the total power.

The increase in temperature of the distilled water/acetic acid mixtureduring the application of the dielectric field is represented by thefollowing equation:

$\begin{matrix}{{\Delta \; T_{3}} = \frac{P_{3} \times t_{3}}{16.387\left( {h_{3} \times \rho_{3} \times d_{3}} \right)}} & (62)\end{matrix}$

where

ΔT₃=increase in temperature of mixture in ° C.

P₃=power in mixture in watts due to the dielectric field

t₃=heating time of mixture in seconds

h₃=specific heat of mixture in J/g ° C.

ρ₃=density of mixture in g/cm³

d₃=thickness of mixture in inches.

Using the power in the distilled water/acetic acid mixture derived aboveand assuming that the specific heat of the distilled water/acetic acidmixture is 3.85 (i.e., (4.18×0.8342)+(2.18×0.1658)) and that the densityof the distilled water/acetic acid mixture is 1.008 (i.e.,(1.0×0.8342)+(1.05×0.1658)), the increase in temperature of thedistilled water/acetic acid mixture during the application of thedielectric field is expressed as follows:

$\begin{matrix}{{\Delta \; T_{3\;}} = {\frac{3.166 \times t_{3}}{16.387\left( {3.85 \times 1.008 \times 4} \right)} = {0.01249 \times t_{3}\mspace{14mu} {^\circ}\mspace{14mu} {C.}}}} & (63)\end{matrix}$

Exemplary Change in Temperature After 7 Seconds

As set forth above, the increase in temperature of the chest region,shoulder region and distilled water/acetic acid mixture during theapplication of the dielectric field are expressed as follows:

ΔT ₁=0.4552×t ₁° C.  (64)

ΔT ₂=0.4552×t ₂° C.  (65)

ΔT ₃=0.01249×t ₃° C.  (66)

If, for example, the heating time is 7 seconds (i.e., the human body isexposed to the dielectric field for 7 seconds), the increase intemperature of the chest and shoulder regions is 3.18° C. (or 5.73° F.)and the increase in temperature of the distilled water/acetic acidmixture is 0.0874° C. (or 0.157° F.). Thus, if the human body starts at98.6° F. (i.e., body temperature) and the distilled water/acetic acidmixture starts at 77° F., then the temperatures of the chest andshoulder regions and the distilled water/acetic acid mixture are 104.33°F. and 77.157° F., respectively, at the end of the dielectric heatingtreatment.

In this example, it can be seen that the chest and shoulder regions heatat the same rate. It can also be seen that the temperature of thedistilled water/acetic acid mixture is relatively low at the end of thedielectric, heating treatment (i.e., 77.157° F.). Accordingly, thedistilled water/acetic acid mixture does not heat the skin of the humanbody during the dielectric heating treatment and also serves to cool thebody upon completion of the dielectric heating treatment. Further, thedistilled water/acetic acid mixture may be chilled prior to, duringand/or after the dielectric heating treatment so as to provide an evengreater cooling effect on the human body.

Other Sub-Regions of the Treatment Region

In this case, the current passing through the chest and shoulder regionsis the same, i.e., 0.24328 amps. It should be understood that there willbe a minor difference between this current and the current passingthrough other sub-regions of the treatment regions if those othersub-regions have different thicknesses. For example, using the aboveequations, it can be calculated that the current passing through asub-region with a thickness of 6 inches is 0.2544 amps (an increase of4.57%) and the current passing through a sub-region with a thickness of2 inches is 0.217 amps (a decrease of 10.8%). These differences areminor and nonetheless result in the application of a substantiallyconstant current across the treatment region. Of course, one skilled inthe art will understand that if the current differences are substantial(e, if a sub-region is unusually thick), it is possible to apply theabove methodology separately to the various sub-regions.

Distilled Water/Acetic Acid Mixture Vs. Air

In the above example, the distilled water/acetic acid mixture injectedinto the bladders in order to obtain a substantially constant currentacross the chest and shoulder regions so that the same cell type in bothregions heats at substantially the same rate. In order to illustrate thebenefits of the distilled water/acetic acid mixture, calculationssimilar to those above are performed for a case in which the shoulderregion is surrounded by air. It is assumed that air has a dielectricconstant of 1 and a dissipation factor of 0. In the following equations,the subscript 2 denotes the shoulder region and the subscript 3′ denotesthe air surrounding the shoulder region. It should be understood thatall of the calculations for the chest region are the same as those inExample 1. It should also be understood that equations (20), (22) and(24) above will not change and, as such, the values of the capacitance,capacitive reactance and resistance of the shoulder region are 3.9864pF, 998.112 ohms and 1,796.6 ohms, respectively.

The capacitance of the air is expressed by the following equation:

$\begin{matrix}{C_{3^{\prime}} = \frac{ɛ_{3^{\prime \;}} \times A \times 0.2249}{d_{3^{\prime}}}} & (67)\end{matrix}$

where

C_(3′)=capacitance of air in picofarads

∈_(3′)=dielectric constant of air

A=area of air in inches²

d_(3′)=thickness of air in inches.

Assuming that the dielectric constant of air is 1 and that the unit areais 1 inch², the capacitance of the air is:

$\begin{matrix}{C_{3^{\prime}} = {\frac{1 \times 1 \times 0.2249}{4} = {0.056\mspace{14mu} {pF}}}} & (68)\end{matrix}$

The capacitive reactance of the air is then given by the followingequation:

$\begin{matrix}{X_{C\; 3^{\prime}} = \frac{1}{2 \times \pi \times f \times C_{3^{\prime \;}}}} & (69)\end{matrix}$

where

X_(C3″)=capacitive reactance of air in ohms

f=frequency of dielectric field in hertz

C_(3′)=capacitance of air in farads.

Using the capacitance of the air derived above and assuming that thefrequency of the dielectric field is 40 MHz, the capacitive reactance ofthe air is:

$\begin{matrix}{X_{C\; 3^{\prime}}^{\prime} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 0.056 \times 10^{- 12}} = {70\text{,}861.5\mspace{14mu} {ohms}}}} & (70)\end{matrix}$

The resistance of the air is equal to the product of the dissipationfactor of the air and the capacitive reactance of the air, as follows:

R _(3′) =df _(3′) ×X _(C3′)  (71)

where

R_(3′)=resistance of air in ohms

df_(3′)=dissipation factor of air

X_(C3′)=capacitive reactance of air in ohms.

Using the capacitive reactance of the air derived above and assumingthat the dissipation factor of air is 0, the resistance of the air isexpressed as follows:

R _(3′)=0×70,861.5=0 ohms  (72)

Next, the current passing between the electrodes through the air (aswell as through the shoulder region) is represented by the followingequation:

$\begin{matrix}{I = \frac{V}{\sqrt{{\left( {X_{c\; 2} + X_{c\; 3^{\prime}}} \right)^{2} + \left( {R_{2} + R_{3^{\prime}}} \right)^{2}}\;}}} & (73)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C2)=capacitive reactance of shoulder region in ohms

X_(C3)=capacitive reactance of air in ohms

R₂=resistance of shoulder region in ohms

R₃=resistance of air in ohms.

Using the capacitive reactance and resistance of each of the shoulderregion and air derived above, and assuming that the voltage between theelectrodes is 1,000 volts, the current passing between the electrodesthrough the air (as well as though the shoulder region) is:

$\begin{matrix}{I = {\frac{1\text{,}000}{\sqrt{\left( {998.112 + {70\text{,}861.5}} \right)^{2} + \left( {{1\text{,}796.6} + 0} \right)^{2}}} = {0.0139\mspace{14mu} {amps}}}} & (74)\end{matrix}$

Now, the power that is dissipated in the shoulder region due to theapplication of the dielectric field is expressed by the followingequation:

P ₂ =R ₂ ×I ²  (75)

where

P₂=power in shoulder region in watts due to the dielectric field

R₂=resistance of shoulder region in ohms

I=current in amperes.

Using the resistance of the shoulder region and the current derivedabove, the power dissipated in the shoulder region due to the dielectricfield is:

P ₂=1,796.6×(0.0139)²=0.3477 watts  (76)

The increase in temperature of the shoulder region during theapplication of the dielectric field is represented by the followingequation:

$\begin{matrix}{{\Delta \; T_{2}} = \frac{P_{2} \times t_{2}}{16.387 \times h_{2} \times \rho_{2} \times d_{2}}} & (77)\end{matrix}$

where

ΔT₂=increase, in temperature of shoulder region in ° C.

P₂=power in shoulder region in watts due to the dielectric field

t₂=heating time of shoulder region in seconds

h₂=specific heat of shoulder region in J/g ° C.

ρ₂=density of shoulder region in g/cm³

d₂=thickness of shoulder region in inches.

Using the power in the shoulder region derived above, and assuming thatthe specific heat and density of the shoulder region are 3.47 J/g° C.and 1.027 g/cm³, respectively, the increase in temperature of theshoulder region during the application of the dielectric, field isexpressed as follows:

$\begin{matrix}{{\Delta \; T_{2}} = {\frac{0.3477 \times t_{2}}{16.387 \times 3.47 \times 1.027 \times 4} = {0.00149 \times t_{2}\mspace{14mu} {^\circ}\mspace{14mu} {C.}}}} & (78)\end{matrix}$

If the heating time is 7 seconds, the increase in temperature of theshoulder region is 0.0104° C. (or 0.0187° F.). Thus, if the human bodystarts at 98.6° F. i.e., body temperature), then the temperature of theshoulder region is 98.6187° F. at the end of the dielectric heatingtreatment. By contrast, as discussed above, the temperature of the chestregion is 104.33° F. at the end of the dielectric heating treatment.Thus, over 300 times more heat is generated in the chest region than theshoulder region and, as a result, the chest region heats at asignificantly faster rate than the shoulder region. Accordingly, it canbe appreciated that the displacement of the air surrounding the shoulderregion with the distilled water/acetic acid mixture is necessary toobtain a substantially constant current across the chest and shoulderregions so that the same cell type in both regions heats atsubstantially the same rate.

2. Treatment Region Contains Varying Amounts of Fat

a. Exemplary Apparatus

Referring to FIGS. 7 a and 7 b, a diagram of an exemplary apparatus thatmay be used to generate a dielectric field between two electrodes andacross a treatment region that contains varying amounts of fat isdesignated as reference numeral 60. Apparatus 60 includes a topelectrode 62 and a bottom electrode 64, both of which are connected toan energy source or generator 66 operable to generate a dielectric fieldbetween the electrodes. Preferably, the voltage between top electrode 62and bottom electrode 64 is substantially constant, which is accomplishedby centering the treatment region at a position that is ¼λ or,alternatively, ¼λ plus a multiple of ¼λ, from the power tube ofgenerator 66 (as discussed above in connection with FIG. 1) or providingmultiple points at this position (as discussed above in connection withFIG. 3). As can be seen, top electrode 62 and bottom electrode 64 eachcomprise a plate, and disposed between the electrodes is a top bladder68 (attached to top electrode 62) and a bottom bladder 70 (attached tobottom electrode 64). Top and bottom bladders 68, 70 may be made of anyflexible and stretchable material, such as silicone rubber or liquidsilicone rubber sold by Rhodia Silicones, so that the bladders are ableto stretch when filled with a flowable material.

Bottom bladder 70 is continuous in the sense that a single bottombladder extends across the surface area of bottom electrode 64. However,top bladder 68 includes multiple compartments located adjacent to thetreatment region. In the illustrated embodiment, top bladder 68 includesforty-eight compartments arranged in a matrix of twelve rows and fourcolumns. Only one of the four columns can be seen in FIGS. 7 a and 7 b,and the twelve rows have been labeled 68 a-68 l. Each compartment has awidth of 6 inches and a length of 6 inches such that the compartmentscollectively extend across the surface area of top electrode 62. Ofcourse, one skilled in the art will appreciate that any number ofcompartments with various dimensions may be used in accordance with thepresent invention, which will vary depending on the size of thetreatment region. One skilled in the art will appreciate that a largernumber of compartments with smaller dimensions will enable the body tobe broken down into a larger number of sub-regions within the treatmentregion.

As shown in FIG. 7 b, the treatment region in the illustrated embodimentcomprises a human body with one or more sub-regions that contain anamount of fat. The body is placed within the cavity between top andbottom bladders 68, 70, and various flowable materials (discussed below)are injected into the compartments of top bladder 68 and into bottombladder 70 so as to displace the air between the body and electrodes. Assuch, the top of the body is in contact with top bladder 68 and thebottom of the body is in contact with bottom bladder 70. One skilled inthe art will appreciate that apparatus 60 may have a variety ofdifferent structural configurations that are encompassed by the presentinvention. It should also be understood that the treatment region maycomprise only a portion of a body that is positioned between theelectrodes of apparatus 60.

b. General Methodology II

For cases in which the treatment region includes two or more sub-regionsthat contain different amounts of fat, a different methodology is usedin order to accommodate for the different amounts of fat. In this case,the treatment region is placed in apparatus 60 shown in FIG. 7 a, andvarious flowable materials (described below) are injected into thecompartment(s) of top bladder 68 and into bottom bladder 70. Thecompositions of the flowable materials, which will vary depending on theamount of fat (if any) located in the various sub-regions, are chosen soas to obtain a substantially constant current across the treatmentregion so that the same cell type in different sub-regions of thetreatment region heats at substantially the same rate.

In accordance with this methodology, a flowable material with a highdielectric constant is injected into the compartment(s) of top bladder68 adjacent any sub-region that contains an amount of fat (assuming thatthe amount of fat in the sub-region is constant). Preferably, theflowable material has a dielectric constant greater than 30, morepreferably greater than 70, and most preferably greater than 100. Thecomposition of the flowable material is calculated so as to allow asubstantially constant current to be applied across the treatmentregion. For example, it will be seen in Example 2 below that theflowable material comprises a mixture of 77.62% hydrogen peroxide and22.4% distilled water. It should be understood that a flowable materialwith a higher dielectric constant will allow this methodology to be usedwith a greater amount of fat. It should also be understood that if thereare multiple sub-regions that contain different amounts of fat, then thecomposition of the flowable material will be different in the varioussub-regions (e.g., the percentages of hydrogen peroxide and distilledwater will vary depending on the amount of fat).

Also, the compartment(s) of top bladder 68 adjacent a sub-region that issubstantially fat-free are filled with a flowable material thatsimulates the body, i.e., either (i) a flowable material having adissipation factor and dielectric constant that are substantially thesame as the body e.g., if the body comprises a human body and thedielectric field has a frequency of 40 MHz, the dissipation factor anddielectric constant of the flowable material are about 1.8 and about 71,respectively) or (ii) a flowable material having a low dissipationfactor (i.e., a dissipation factor preferably less than 1.0, morepreferably less than 0.5, and most preferably less than 0.3) and adielectric constant that are selected such that the flowable materialsimulates the body (e.g., 83.42% distilled water and 16.58% acetic acid,as calculated in Example 1 above). This same flowable material is alsoinjected into bottom bladder 70. Of course, if the thickness of such asub-region is the same as the spacing between the electrodes (as inExample 2 below), then there is no need to inject the flowable materialinto the adjacent compartment(s) of top bladder 68.

In addition, the compartment(s) of top bladder 68 adjacent a region thatdoes not require treatment are filled with air or another flowablematerial with a very low dielectric constant in order to significantlyreduce the current in the region. Preferably, the flowable material hasa dielectric constant less than 10, more preferably less than 6, andmost preferably less than 4 (e.g., air has a dielectric constant ofabout 1).

Example 2

An example using this general methodology is provided below in which ahuman body is placed in apparatus 60 shown in FIG. 7 a, wherein thetreatment region includes the chest and stomach regions of the body. Thechest region, (which is substantially fat-free) has a thickness of 8inches, and the stomach region has a thickness of 6⅜ inches, whichincludes 6 inches of non-fatty tissue and ⅜ inches of fat. For the sakeof clarity, the 6 inches of non-fatty tissue (e.g., epidermal/dermalskin cells, stomach cells, circulatory cells, etc) in the stomach regionwill be referred to hereinafter as the “stomach region,” and the ⅜inches of fat (e.g., adipose tissue) will be referred to hereinafter asthe “stomach fat.”

The top and bottom electrodes 62 and 44 are spaced 8 inches apart, andthe voltage between the electrodes is 1,000 volts. The compartments oftop bladder 68 located adjacent the chest region (i.e., the row ofcompartments labeled 68 d) are empty because the thickness of the chestregion is the same as the spacing between the electrodes. A flowablematerial comprising hydrogen peroxide mixed with distilled water isinjected into the compartments of top bladder 68 adjacent the stomachregion/stomach fat i.e., the two rows of compartments labeled 68 e and68 f) and into bottom bladder 70. Accordingly, the material between theelectrodes in the chest region is the human body i.e., the 8 inch chestregion) and the material between the electrodes in the stomach region isthe human body and the hydrogen peroxide/distilled water mixture (i.e.,the 6 inch stomach region, the ⅜ inch stomach fat, and 1⅝ inches of thehydrogen peroxide/distilled water mixture). In this example, air isinjected into the remaining compartments of top bladder 68, which willresult in minimal heating of the remaining regions of the body.

The following table identifies the dielectric constant, dissipationfactor, specific heat and density of each of the materials between theelectrodes, assuming that the frequency of the dielectric field is 40MHz:

Dielectric Dissipation Specific Heat Density Constant Factor (J/g ° C.)(g/cm³) Human Body 71 1.8 3.47 1.027 (Chest and Stomach Regions) HumanBody 11 1.1 1.93 0.918 (Stomach Fat) Hydrogen 128 .04 2.619 1.463Peroxide Distilled 76 .005 4.18 1 Water

In order to obtain a substantially constant current across the chest andstomach regions of the body so that the same cell type in both regionsheats at substantially the same rate, the current passing through thestomach region, stomach fat and surrounding hydrogen peroxide/distilledwater mixture must be substantially the same as the current passingthrough the chest region. The following calculations are performed todetermine the volume of hydrogen peroxide and the volume of distilledwater that will result in a substantially constant current across thechest and stomach regions of the body. In the following equations, thesubscript 1 denotes the chest region of the body, the subscript 2denotes the stomach region of the body, the subscript 3 denotes thestomach fat, and the subscript 4 denotes the hydrogen peroxide/distilledwater mixture (wherein the subscript hp denotes the hydrogen peroxideand the subscript dw denotes the distilled water in certain equations).

Calculations for Chest Region

The capacitance, capacitive reactance and resistance of the chest regionare the same as those calculated in equations (7), (9) and (11) ofExample 1 above, as follows:

C ₁=1.9932 pF  (79)

X _(C1)=1,996.2 ohms  (80)

R ₁=3,593.2 ohms  (81)

Also, the current passing between the electrodes through the chestregion and the power dissipated in the chest region due to theapplication of the dielectric field are the same as those calculated inequations (13) and (15) of Example 1 above, as follows:

I=0.24328 amps  (82)

P ₁=212.67 watts  (83)

In addition, the increase in temperature of the chest region during theapplication of the dielectric field is the same as that calculated inequation (18) of Example 1, as follows:

ΔT ₁=0.4552×t ₁° C.  (84)

Calculations for Stomach Region, Stomach Fat and HydrogenPeroxide/Distilled Water Mixture

The capacitance of the stomach region is expressed by the followingequation:

$\begin{matrix}{C_{2} = \frac{ɛ_{2} \times A \times 0.2249}{d_{2}}} & (85)\end{matrix}$

where

C₂=capacitance of stomach region in picofarads

∈₂=dielectric constant of stomach region

A=area of stomach region in inches²

d₂=thickness of stomach region in inches.

Assuming that the dielectric constant of the stomach region is 71 andthat the unit area is 1 inch², the capacitance of the stomach region is:

$\begin{matrix}{C_{2} = {\frac{71 \times 1 \times 0.2249}{6} = {2.6576\mspace{14mu} {{pF}.}}}} & (86)\end{matrix}$

The capacitive reactance of the stomach region is then given by thefollowing equation:

$\begin{matrix}{X_{C\; 2} = \frac{1}{2 \times \pi \times f \times C_{2\;}}} & (87)\end{matrix}$

where

X_(C2)=capacitive reactance of stomach region in ohms

f=frequency of dielectric field in hertz

C₂=capacitance of stomach region in farads.

Using the capacitance of the stomach region derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the stomach region is:

$\begin{matrix}{X_{C\; 2} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 2.6576 \times 10^{- 12}} = {1,497.2\mspace{14mu} {ohms}}}} & (88)\end{matrix}$

The resistance of the stomach region is equal to the product of thedissipation factor of the stomach region and the capacitive reactance ofthe stomach region, as follows:

R ₂ =df ₂ ×X _(C2)  (89)

where

R₂=resistance of stomach region in ohms

df₂=dissipation factor of stomach region

X_(C2)=capacitive reactance of stomach region in ohms.

Using the capacitive reactance of the stomach region derived above andassuming that the dissipation factor of the stomach region is 1.8, theresistance of the stomach region is expressed as follows:

R ₂=1.8×1,497.2=2,694.96 ohms  (90)

Now, the capacitance of the stomach fat is expressed by the followingequation:

$\begin{matrix}{C_{3} = \frac{ɛ_{3} \times A \times 0.2249}{d_{3}}} & (91)\end{matrix}$

where

C₃=capacitance of stomach fat in picofarads

∈₃=dielectric constant of stomach fat

A=area of stomach fat in inches²

d₃=thickness of stomach fat in inches.

For a unit area of 1 inch², the capacitance of the stomach fat is:

$\begin{matrix}{C_{3} = {\frac{11 \times 1 \times 0.2249}{0.375} = {6.588\mspace{14mu} {pF}}}} & (92)\end{matrix}$

The capacitive reactance of the stomach fat is then given by thefollowing equation:

$\begin{matrix}{X_{C\; 3} = \frac{1}{2 \times \pi \times f \times C_{3}}} & (93)\end{matrix}$

where

X_(C3)=capacitive reactance of stomach fat in ohms

f=frequency of dielectric field in hertz

C₃=capacitance of stomach fat in farads.

Using the capacitance of the stomach fat derived above and assuming thatthe frequency of the dielectric field is 40 MHz, the capacitivereactance of the stomach fat is:

$\begin{matrix}{X_{C\; 3} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times ɛ_{3} \times 6.588 \times 10^{- 12}} = {603.96\mspace{14mu} {ohms}}}} & (94)\end{matrix}$

The resistance of the stomach fat is equal to the product of thedissipation factor of the stomach fat and the capacitive reactance ofthe stomach fat, as follows:

R ₃ =df ₃ ×X _(C3)  (95)

where

R₃=resistance of stomach fat in ohms

df₃=dissipation factor of stomach fat

X_(C3)=capacitive reactance of stomach fat in ohms.

Using the capacitive reactance of the stomach fat derived above, theresistance of the stomach fat is:

R ₃=1.1×603.96=664.4 ohms  (96)

Now, assume that the hydrogen peroxide/distilled water mixture consistsof a volume of hydrogen peroxide represented by x and a volume ofdistilled water represented by 1−x. The capacitance of the hydrogenperoxide is expressed by the following equation:

$\begin{matrix}{C_{hp} = \frac{ɛ_{hp} \times A \times 0.2249}{d_{hp}}} & (97)\end{matrix}$

where

C_(hp)=capacitance of hydrogen peroxide in picofarads,

∈_(hp)=dielectric constant of hydrogen peroxide

A=area of hydrogen peroxide in inches²

d_(hp)=thickness of hydrogen peroxide in inches.

For a unit area of 1 inch², the capacitance of the hydrogen peroxide is:

$\begin{matrix}{C_{hp} = {\frac{128 \times 1 \times 0.224}{1.625 \times x} = {\frac{17.69}{x}\mspace{14mu} {pF}}}} & (98)\end{matrix}$

Similarly, the capacitance of the distilled water is expressed by thefollowing equation:

$\begin{matrix}{C_{dw} = \frac{ɛ_{dw} \times A \times 0.2249}{d_{dw}}} & (99)\end{matrix}$

where

C_(dw)=capacitance of distilled water in picofarads

∈_(dw)=dielectric constant of distilled water

A=area of distilled water in inches²

d_(dw)=thickness of distilled water in inches.

For a unit area of 1 inch², the capacitance of the distilled water is:

$\begin{matrix}{C_{dw} = {\frac{76 \times 1 \times 0.2249}{1.625\left( {1 - x} \right)} = {\frac{10.5}{1 - x}\mspace{14mu} {pF}}}} & (100)\end{matrix}$

The capacitive reactance of the hydrogen peroxide is given by thefollowing equation:

$\begin{matrix}{X_{Chp} = \frac{1}{2 \times \pi \times f \times C_{hp}}} & (101)\end{matrix}$

where

X_(Chp)=capacitive reactance of hydrogen peroxide in ohms

f=frequency of dielectric field in hertz

C_(hp)=capacitance of hydrogen peroxide in farads.

Using the capacitance of the hydrogen peroxide derived above andassuming that the frequency of the dielectric field is 40 MHz, thecapacitive reactance of the hydrogen peroxide is:

$\begin{matrix}{X_{Chp} = {\frac{x}{2 \times \pi \times 40 \times 10^{6} \times 17.69 \times 10^{- 12}} = {224.9x\mspace{11mu} {ohms}}}} & (102)\end{matrix}$

Similarly, the capacitive reactance of the distilled water is then givenby the following equation:

$\begin{matrix}{X_{Cdw} = \frac{1}{2 \times \pi \times f \times C_{dw}}} & (103)\end{matrix}$

where

X_(Cdw)=capacitive reactance of distilled water in ohms

f=frequency of dielectric field in hertz

C_(dw)=capacitance of distilled water in farads.

Using the capacitance of the distilled water derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the distilled water is:

$\begin{matrix}{X_{Cdw} = {\frac{1 - x}{2 \times \pi \times 40 \times 10^{6} \times 10.5 \times 10^{- 12}} = {378.9\left( {1 - x} \right)\mspace{11mu} {ohms}}}} & (104)\end{matrix}$

Now, the total capacitive reactance of the hydrogen peroxide/distilledwater mixture is expressed as follows:

X _(C4) =X _(Chp) +X _(Cdw)  (105)

where

X_(C4)=capacitive reactance of mixture in ohms

X_(Chp)=capacitive reactance of hydrogen peroxide in ohms

X_(Cdw)=capacitive reactance of distilled water in ohms.

Using the capacitive reactance of each of the hydrogen peroxide anddistilled water derived above, the capacitive reactance of the hydrogenperoxide/distilled water mixture is:

X _(C4)=(224.9x)+(378.9(1−x))=378.9−154x ohms  (106)

The resistance of the hydrogen peroxide is equal to the product of thedissipation factor of the hydrogen peroxide and the capacitive reactanceof the hydrogen peroxide, as follows:

R _(hp) =df _(hp) ×X _(Chp)  (107)

where

R_(hp)=resistance of hydrogen peroxide in ohms

df_(hp)=dissipation factor of hydrogen peroxide

X_(Chp)=capacitive reactance of hydrogen: peroxide in ohms.

Using the capacitive reactance of the hydrogen peroxide derived aboveand assuming that the dissipation factor of hydrogen peroxide is 0.04,the resistance of the hydrogen peroxide is:

R _(hp)=0.04×224.9x=9x ohms  (108)

Similarly, the resistance of the distilled water is equal to the productof the dissipation factor of the distilled, water and the capacitivereactance of the distilled water, as follows:

R _(dw) =df _(dw) ×X _(Cdw)  (109)

where

R_(dw)=resistance of distilled water in ohms

df_(dw)=dissipation factor of distilled water

X_(Cdw)=capacitive reactance of distilled water in ohms.

Using the capacitive reactance of the distilled water derived above andassuming that the dissipation factor of distilled water is 0.005, theresistance of the distilled water is:

R _(dw)=0.005×378.9(1−x)=1.89(1−x) ohms  (110)

Now, the total resistance of the hydrogen peroxide/distilled watermixture is expressed as follows:

R ₄ =R _(hp) +R _(dw)  (111)

where

R₄=resistance of mixture in ohms

R_(hp)=resistance of hydrogen peroxide in ohms

R_(dw)=resistance of distilled water in ohms.

Using the resistance of each of the hydrogen peroxide and distilledwater derived above, the resistance of the hydrogen peroxide/distilledwater mixture is:

R ₄=(9x)+(1.89(1−x))=1.89−7.11x ohms  (112)

Next, the current passing between the electrodes through the hydrogenperoxide/distilled water mixture, stomach fat and stomach region isrepresented by the following equation:

$\begin{matrix}{I = \frac{V}{\sqrt{\left( {X_{C\; 2} + X_{C\; 3} + X_{C\; 4}} \right)^{2} + \left( {R_{2} + R_{3} + R_{4}} \right)^{2}}}} & (113)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C2)=capacitive reactance of stomach region in ohms

X_(C3)=capacitive reactance of stomach fat in ohms

X_(C4)=capacitive reactance of mixture in ohms

R₂=resistance of stomach region in ohms

R₃=resistance of stomach fat in ohms

R₄=resistance of mixture in ohms.

The current passing between the electrodes through the hydrogenperoxide/distilled water mixture, stomach fat and stomach region must besubstantially the same as the current passing between the electrodesthrough the chest region. Using the current passing between theelectrodes through the chest region derived above, using the capacitivereactance and resistance of each of the stomach region, stomach fat andhydrogen peroxide/distilled; mixture derived above, and assuming thatthe voltage between the electrodes is 1,000 volts, the current passingbetween the electrodes through the hydrogen peroxide/distilled watermixture, stomach fat and stomach region is:

$\begin{matrix}{0.24328 = {\frac{1,000}{\sqrt{\left( {{2,480.06} - {154x}} \right)^{2} + \left( {{3,361.25} + {7.11x}} \right)^{2}}}\mspace{14mu} {amps}}} & (114)\end{matrix}$

By solving equation (114) for x, it can be seen that the volume ofhydrogen peroxide represented by x is 0.776 and, thus, the volume ofdistilled water represented by (1−x) is 0.224. In other words, thehydrogen peroxide/distilled water mixture is 77.62% hydrogen peroxide(by volume) and 22.4% distilled water (by volume).

The power that is dissipated in the stomach region due to theapplication of the dielectric field is expressed by the followingequation:

P ₂ =R ₂ ×I ²  (115)

where

P₂=power in stomach region in watts due to the dielectric field

R₂=resistance of stomach region in ohms

I=current in amperes.

Using the resistance of the stomach region and the current derivedabove, the power dissipated in the stomach region due to the dielectricfield is:

P ₂=(2,694.96)×(0.24328)²=159.45 watts  (116)

The increase in temperature of the stomach region during the applicationof the dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{2}} = \frac{P_{2} \times t_{2}}{16.387\left( {h_{2} \times \rho_{2} \times d_{2}} \right)}} & (117)\end{matrix}$

where

ΔT₂=increase in temperature of stomach region in ° C.

P₂=power in stomach region in watts due to the dielectric field.

t₂=heating time of stomach region in seconds

h₂=specific heat of stomach region in J/g ° C.

ρ₂=density of stomach region in g/cm³

d₂=thickness of stomach region in inches.

Using the power in the stomach region derived above and assuming thatthe specific heat and density of the stomach region are 3.47 J/g° C. and1.027 g/cm³, respectively, the increase in temperature of the stomachregion during the application of the dielectric field is expressed asfollows:

$\begin{matrix}{{\Delta \; T_{2}} = {\frac{159.45 \times t_{2}}{16.387\left( {3.47 \times 1.027 \times 6} \right)} = {0.4552 \times t_{2}\mspace{11mu} {^\circ}\mspace{14mu} {C.}}}} & (118)\end{matrix}$

Similarly, the power that is dissipated in the stomach fat due to theapplication of the dielectric field is expressed by the followingequation:

P ₃ =R ₃ ×I ²  (119)

where

P₃=power in stomach fat in watts due to the dielectric field

R₃=resistance of stomach fat in ohms

I=current in amperes.

Using the resistance of the stomach fat and the current derived above,the power dissipated in the stomach fat due to the dielectric field is:

P ₃=(664.4)×(0.24328)²=39.32 watts  (120)

The increase in temperature of the stomach fat during the application ofthe dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{3}} = \frac{P_{3} \times t_{2}}{16.387\left( {h_{3} \times \rho_{3} \times d_{3}} \right)}} & (121)\end{matrix}$

where

ΔT₃=increase in temperature of stomach fat in ° C.

P₃=power in stomach fat in watts due to the dielectric field

t₃=heating time of stomach fat in seconds

h₃=specific heat of stomach fat in J/g ° C.

ρ₃=density of stomach fat in g/cm³

d₃=thickness of stomach fat in inches.

Using the power in the stomach fat derived above and assuming that thespecific heat and density of the stomach fat are 1.93 J/g ° C. and 0.918g/cm³, respectively, the increase in temperature of the stomach fatduring the application of the dielectric field is expressed as follows:

$\begin{matrix}{{\Delta \; T_{3}} = {\frac{39.32 \times t_{3}}{16.387\left( {1.93 \times 0.918 \times 0.375} \right)} = {3.61 \times t_{3}\mspace{11mu} {^\circ}\mspace{14mu} {C.}}}} & (122)\end{matrix}$

Similarly, the power that is dissipated in the hydrogenperoxide/distilled water mixture due to the application of thedielectric field is expressed by the following equation:

P ₄ =R ₄ ×I ²  (123)

where

P₄=power in mixture in watts due to the dielectric field

R₄=resistance of mixture in ohms

I=current in amperes.

Using the resistance of the hydrogen peroxide/distilled water mixture(with x=0.776) and the current derived above, the power dissipated inthe hydrogen peroxide/distilled water mixture due to the dielectricfield is:

P ₄=(2.957)×(0.24328)²=0.438 watts  (124)

The increase in temperature of the hydrogen peroxide/distilled watermixture during the application of the dielectric field is represented bythe following equation:

$\begin{matrix}{{\Delta \; T_{4}} = \frac{P_{4} \times t_{4}}{16.387\left( {h_{4} \times \rho_{4} \times d_{4}} \right)}} & (125)\end{matrix}$

where

ΔT₄=increase in temperature of mixture in ° C.

P₄=power in mixture in watts due to the dielectric field

t₄=heating time of mixture n in seconds

h₄=specific heat of mixture in J/g ° C.

ρ₄=density of mixture in g/cm³

d₄=thickness of mixture in inches.

Using the power in the hydrogen peroxide/distilled water mixture derivedabove and assuming that the specific heat of the hydrogenperoxide/distilled water mixture is 2.969 (i.e.,(2.619×0.776)+(4.18×0.224)) and that the density of the hydrogenperoxide/distilled water mixture is 1.359 (i.e.,(1.463×0.776)+(1×0.224)), the increase in temperature of the hydrogenperoxide/distilled water mixture during the application of thedielectric field is expressed as follows:

$\begin{matrix}{{\Delta \; T_{4}} = {\frac{0.438 \times t_{4}}{16.387\left( {2.969 \times 1.359 \times 1.625} \right)} = {0.004 \times t_{4}\mspace{11mu} {^\circ}\mspace{14mu} {C.}}}} & (126)\end{matrix}$

Exemplary Change in Temperature after 7 Seconds

As set forth above, the increase in temperature of the chest region,stomach region, stomach fat and hydrogen peroxide/distilled watermixture during the application of the dielectric field are expressed asfollows:

ΔT ₁=0.4552×t ₁° C.  (127)

ΔT ₂=0.4552×t ₂° C.  (128)

ΔT ₃=3.61×t ₃° C.  (129)

ΔT ₄=0.004×t ₄° C.  (130)

If, for example, the heating time is 7 seconds (i.e., the human body isexposed to the dielectric field for 7 seconds), the increase intemperature of the chest and stomach regions is 3.18° C. (or 5.73° F.),the increase in temperature of the stomach fat is 25.28° C. (or 45.5°F.), and the increase in temperature of the hydrogen peroxide/distilledwater mixture is 0.0285° C. (or 0.05° F.). Thus, if the human bodystarts at 98.6° F. (i.e., body temperature) and the hydrogenperoxide/distilled water mixture starts at 77° F., then the temperaturesof the chest and stomach regions, stomach fat and the hydrogenperoxide/distilled water mixture are 104.33° F., 123.88° F. and 77.05°F., respectively, at the end of the dielectric heating treatment.

In this example, it can be seen that the chest and stomach regions heatat the same rate. The stomach fat heats at a much faster rate and willliquefy during the dielectric heating treatment. Preferably, theliquefied stomach fat is removed from the body through any means knownin the art (e.g., syringe or liposuction). It can also be seen that thetemperature of the hydrogen peroxide/distilled water mixture isrelatively low at the end of the dielectric heating treatment (i.e.,77.05° F.). Accordingly, the hydrogen peroxide/distilled water mixturedoes not heat the skin of the human body during the dielectric heatingtreatment and also serves to cool the body upon completion of thedielectric heating treatment. Further, the hydrogen peroxide/distilledwater mixture may be chilled prior to, during and/or after thedielectric heating treatment so as to provide an even greater coolingeffect on the human body.

c. General Methodology III

There are cases in which the amount of fat in a sub-region (e.g., thestomach region) is large enough that it would be difficult to obtain asubstantially constant current across the treatment region using thegeneral methodology described above. As such, for larger amounts of fat,a different methodology is used in which a treatment region is placed inapparatus 60 shown in FIG. 7 a, and a conductive flowable material isinjected into the compartment(s) of top bladder 68 adjacent anysub-region with a large amount of fat in order to effectively narrow thegap between the electrodes. Various other flowable materials (describedbelow) are then injected into the other compartment(s) of top bladder 68and into bottom bladder 70. The compositions of the flowable materialsare chosen so as to obtain a substantially constant current across thetreatment region so that the same cell type in different sub-regions ofthe treatment region heats at substantially the same rate.

In accordance with this methodology, the compartment(s) of top bladder68 adjacent any sub-region region that is substantially fat-free arefilled with a flowable material with a low dielectric constant.Preferably, the flowable material has a dielectric constant less than50, more preferably less than 30, and most preferably less than 10. Forexample, it will be seen in Example 3 below that the flowable materialcomprises acetic acid, which has a dielectric constant of 6.2. Ofcourse, other flowable materials may be used including, but not limitedto, a mixture of distilled water and acetic, acid. The thickness of theflowable material is calculated so as to allow a substantially constantcurrent to be applied across the treatment region. It should beunderstood that the thickness of the flowable material will depend onthe dielectric constant of the flowable material. Specifically, aflowable material with a higher dielectric constant will require agreater thickness of the flowable material, and a flowable material witha lower dielectric constant will require a smaller thickness of theflowable material.

Also, bottom bladder (70) is filled with a flowable material thatsimulates the body, i.e., either (i) a flowable material having adissipation factor and dielectric constant that are substantially thesame as the body (e.g., if the body comprises a human body and thedielectric field has a frequency of 40 MHz, the dissipation factor anddielectric constant of the flowable material are about 1.8 and about 71,respectively) or (ii) a flowable material having a low dissipationfactor (i.e., a dissipation factor preferably less than 1.0, morepreferably less than 0.5, and most preferably less than 0.3) and adielectric constant that are selected such that the flowable materialsimulates the body (e.g., 83.42% distilled water and 16.58% acetic acid,as calculated in Example 1 above).

In addition, the compartment(s) of top bladder 68 adjacent a region thatdoes not require treatment are filled with air or another flowablematerial with a very low dielectric constant in order to significantlyreduce the current in the region. Preferably, the flowable material hasa dielectric constant less than 10, more preferably less than 6, andmost preferably less than 4 (e.g., air has a dielectric constant ofabout 1).

Example 3

An example using this general methodology is provided below in which ahuman body is placed in apparatus 60 shown in FIG. 7 a, wherein thetreatment region includes the chest and stomach regions of the body. Thechest region (which is substantially fat-free) has a thickness of 8inches, and the stomach region has a thickness of 8 inches, whichincludes 7 inches of non-fatty tissue and 1 inch of fat. For the sake ofclarity, the 7 inches of non-fatty tissue (e.g., epidermal/dermal skincells, stomach ells, circulatory cells, etc) in the stomach region willbe referred to hereinafter as the “stomach region,” and the 1 inch offat (e.g., adipose tissue) will be referred to hereinafter as the“stomach fat.”

Acetic acid is injected into the compartments of top bladder 68 adjacentthe chest region (e.g., the row of compartments labeled 68 d) and intobottom bladder 70. Then, the compartments of top bladder 68 adjacent thestomach region/stomach fat (e.g., the two rows of compartments labeled68 e and 68 f) are filled with a liquid conductor to effectively narrowthe spacing between the electrodes in this sub-region. In this example,the liquid conductor comprises a eutectic compound consisting of 62.5%gallium, 21.5% indium and 16.0% tin (made by MCP Metal SpecialtiesInc.). Air is injected into the remaining compartments of top bladder68, which will result in minimal heating of the remaining regions of thebody. In this example, the voltage between the top and bottom electrodes62 and 64 is 1,000 volts.

The following table identifies the dielectric constant, dissipationfactor, specific heat and density of each of the materials between theelectrodes, assuming that the frequency of the dielectric field is 40MHz:

Dielectric Dissipation Specific Heat Density Constant Factor (J/g ° C.)(g/cm³) Human Body 71 1.8 3.47 1.027 (Chest and Stomach Regions) HumanBody 11 1.1 1.93 0.918 (Stomach Fat) Acetic Acid 6.2 0.0262 2.18 1.05

In order to obtain a substantially constant current across the chest andstomach regions of the body so that the same cell type in both regionsheats at substantially the same rate, the current passing through thestomach fat and stomach region must be substantially the same as thecurrent passing through the acetic acid and chest region. The followingcalculations are performed to determine the thickness of the acetic acidthat will result in a substantially constant current across the chestand stomach regions of the body (wherein the same thickness of liquidconductor will also be used). In the following equations, the subscript1 denotes the acetic acid, the subscript 2 denotes the chest region ofthe body, the subscript 3 denotes the stomach region of the body, andthe subscript 4 denotes the stomach fat.

Calculations for Acetic Acid and Chest Region

First, the capacitance of the acetic acid is expressed by the followingequation:

$\begin{matrix}{C_{1} = \frac{ɛ_{1} \times A \times 0.2249}{d_{1}}} & (131)\end{matrix}$

where

C₁=capacitance of acetic acid in picofarads

∈₁=dielectric constant of acetic acid

A=area of acetic acid in inches²

d₁=thickness of acetic acid in inches.

Assuming that the dielectric constant of the acetic acid is 6.2 and thatthe unit area is 1 inch², the capacitance of the acetic acid is:

$\begin{matrix}{C_{1} = {\frac{6.2 \times 1 \times 0.2249}{d_{1}} = {\frac{1.39}{d_{1}}\mspace{14mu} {pF}}}} & (132)\end{matrix}$

Similarly, the capacitance of the chest region is expressed by thefollowing equation:

$\begin{matrix}{C_{2} = \frac{ɛ_{2} \times A \times 0.2249}{d_{2}}} & (133)\end{matrix}$

where

C₂=capacitance of chest region in picofarads

∈₂=dielectric constant of chest region

A=area of chest region in inches²

d₂=thickness of chest region in inches.

Assuming that the dielectric constant of the chest region is 71 and thatthe unit area is 1 inch², the capacitance of the chest region is:

$\begin{matrix}{C_{2} = {\frac{71 \times 1 \times 0.2249}{8} = {1.993\mspace{14mu} {pF}}}} & (134)\end{matrix}$

The capacitive reactance of the acetic acid is given by the followingequation:

$\begin{matrix}{X_{C\; 1} = \frac{1}{2 \times \pi \times f \times C_{1}}} & (135)\end{matrix}$

where

X_(C1)=capacitive reactance of acetic acid in ohms.

f=frequency of dielectric field in hertz

C₁=capacitance of acetic acid in farads.

Using the capacitance of the acetic acid derived above and assuming thatthe frequency of the dielectric field is 40 MHz, the capacitivereactance of the acetic acid is:

$\begin{matrix}{X_{C\; 1} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times \frac{1.39 \times 10^{- 12}}{d_{1}}} = {2\text{,}857.6 \times d_{1}\mspace{14mu} {ohms}}}} & (136)\end{matrix}$

Similarly, the capacitive reactance of the chest region is given by thefollowing equation:

$\begin{matrix}{X_{C\; 2} = \frac{1}{2 \times \pi \times f \times C_{2}}} & (137)\end{matrix}$

where

X_(C2)=capacitive reactance of chest region in ohms

f=frequency of dielectric field in hertz

C₂=capacitance of chest region in farads.

Using the capacitance of the chest region derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the chest region is:

$\begin{matrix}{X_{C\; 2} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 1.993 \times 10^{- 12}} = {1\text{,}996.4\mspace{14mu} {ohms}}}} & (138)\end{matrix}$

Then, the total capacitive reactance of the acetic acid and chest regionis obtained by adding equations (136) and (138), as follows:

X _(C1,C2)=2,857.6d ₁+1,996.4 ohms  (139)

The resistance of the acetic acid is equal to the product of thedissipation factor of the acetic acid and the capacitive reactance ofthe acetic acid, as follows:

R ₁ =df ₁ ×X _(C1)  (140)

where

R₁=resistance of acetic acid in ohms

df₁=dissipation factor of acetic acid

X_(C1)=capacitive reactance of acetic acid in ohms.

Using the capacitive reactance of the acetic acid derived above andassuming that the dissipation factor of the acetic acid is 0.0262, theresistance of the acetic acid is expressed as follows:

R ₁=0.0262×2,857.6×d ₁=74.87×d ₁ ohms  (141)

Similarly, the resistance of the chest region is equal to the product ofthe dissipation factor of the chest region and the capacitive reactanceof the chest region, as follows:

R ₂ =df ₂ ×X _(C2)  (142)

where

R₂=resistance of chest region in ohms

df₂=dissipation factor of chest region

X_(C2)=capacitive reactance of chest region in ohms

Using the capacitive reactance of the chest region derived above andassuming that the dissipation factor of the chest region is 1.8, theresistance of the chest region is expressed as follows:

R ₂=1.8×1,996.4=3,593.52 ohms  (143)

Then, the total resistance of the acetic acid and chest region isobtained by adding equations (141) and (143), as follows:

R _(1.2)=(74.87×d ₁)+3,593.52 ohms  (144)

Next, the current passing between the electrodes through the acetic acidand chest region is represented by the following equation:

$\begin{matrix}{I = \frac{V}{\sqrt{X_{{C\; 1},2}^{2} + R_{1,2}^{2}}}} & (145)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C1,2)=total capacitive reactance of acetic acid/chest region in ohms

R_(1,2)=total resistance of acetic acid/chest region in ohms.

Using the total capacitive reactance and total resistance of the aceticacid and chest region derived above, and assuming that the voltagebetween the electrodes is 1,000 volts, the current passing between theelectrodes through the acetic acid and chest region is:

$\begin{matrix}{I = {\frac{1\text{,}000}{\sqrt{\left( {{1\text{,}996.4} + {2\text{,}857.6d_{1}}} \right)^{2} + \left( {{3\text{,}593.52} + {74.87d_{1}}} \right)^{2}}}\mspace{14mu} {amps}}} & (146)\end{matrix}$

Calculations for Stomach Region and Stomach Fat

The capacitance of the stomach region is expressed by the followingequation:

$\begin{matrix}{C_{3} = \frac{ɛ_{3} \times A \times 0.2249}{d_{3}}} & (147)\end{matrix}$

where

C₃=capacitance of stomach region in picofarads

∈₃=dielectric constant of stomach region

A=area of stomach region in inches²

d₃=thickness of stomach region in inches.

Assuming that the dielectric constant of the stomach region is 71 andthat the unit area is 1 inch², the capacitance of the stomach region is:

$\begin{matrix}{C_{3} = {\frac{71 \times 1 \times 0.2249}{7} = {2.278\mspace{14mu} {pF}}}} & (148)\end{matrix}$

Similarly, the capacitance of the stomach fat is expressed by thefollowing equation:

$\begin{matrix}{C_{4} = \frac{ɛ_{4} \times A \times 0.2249}{d_{4}}} & (149)\end{matrix}$

where

C₄=capacitance of stomach fat in picofarads

∈₄=dielectric constant of stomach fat

A=area of stomach fat in inches²

d₄=thickness of stomach fat in inches.

Assuming that the dielectric constant of the stomach fat is 11 and thatthe unit area is 1 inch², the capacitance of the stomach fat is:

$\begin{matrix}{C_{4} = {\frac{11 \times 1 \times 0.2249}{1} = {2.47\mspace{14mu} {pF}}}} & (150)\end{matrix}$

The capacitive reactance of the stomach region is given by the followingequation:

$\begin{matrix}{X_{C\; 3} = \frac{1}{2 \times \pi \times f \times C_{3}}} & (151)\end{matrix}$

where

X_(C3)=capacitive reactance of stomach region in ohms

f=frequency of dielectric field in hertz

C₃=capacitance of stomach region in farads.

Using the capacitance of the stomach region derived above and assumingthat the frequency of the dielectric field is 40 MHz, the capacitivereactance of the stomach region is:

$\begin{matrix}{X_{C\; 3} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 2.278 \times 10^{- 12}} = {1\text{,}746.7\mspace{14mu} {ohms}}}} & (152)\end{matrix}$

Similarly, the capacitive reactance of the stomach fat is given by thefollowing equation:

$\begin{matrix}{X_{C\; 4} = \frac{1}{2 \times \pi \times f \times C_{4}}} & (153)\end{matrix}$

where

X_(C4)=capacitive reactance of stomach fat in ohms

f=frequency of dielectric field in hertz

C₄=capacitance of stomach fat in farads.

Using the capacitance of the stomach fat derived above and assuming thatthe frequency of the dielectric field is 40 MHz, the capacitivereactance of the stomach fat is:

$\begin{matrix}{X_{C\; 4} = {\frac{1}{2 \times \pi \times 40 \times 10^{6} \times 2.47 \times 10^{- 12}} = {1\text{,}610.9\mspace{14mu} {ohms}}}} & (154)\end{matrix}$

Then, the total capacitive reactance of the stomach region and stomachfat is obtained by adding equations (152) and (154), as follows:

X _(C3,C4)=1,746.7+1,610.9=3,357.6 ohms  (155)

The resistance of the stomach region is equal to the product of thedissipation factor of the stomach region and the capacitive reactance ofthe stomach region, as follows:

R ₃ =df ₃ ×X _(C3)  (156)

where

R₃=resistance of stomach region in ohms

df₃=dissipation factor of stomach region

X_(C3)=capacitive reactance of stomach region in ohms.

Using the capacitive reactance of the stomach region derived above andassuming that the dissipation factor of the stomach region is 1.8, theresistance of the stomach region is expressed as follows:

R ₃=1.8×1,746.7=3,144.06 ohms  (157)

Similarly, the resistance of the stomach fat is equal to the product ofthe dissipation factor of the stomach fat and the capacitive reactanceof the stomach fat, as follows:

R ₄ =df ₄ ×X _(C4)  (158)

where

R₄=resistance of stomach fat in ohms

df₄=dissipation factor of stomach fat

X_(C4)=capacitive reactance of stomach fat in ohms.

Using the capacitive reactance of the stomach fat derived above andassuming that the dissipation factor of the stomach fat is 1.1, theresistance of the stomach fat is expressed as follows:

R ₄=1.1×1,610.9=1,772 ohms  (159)

Then, the total resistance of the stomach region and stomach fat isobtained by adding equations (157) and (159), as follows:

R _(3,4)=3,144.06+1,772=4,916.06 ohms  (160)

Next, the current passing between the electrodes through the stomachregion and stomach fat is represented by the following equation:

$\begin{matrix}{I==\frac{V}{\sqrt{X_{{C\; 3},4}^{2} + R_{3,4}^{2}}}} & (161)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts,

X_(C3,4)=total capacitive reactance of stomach region/stomach fat inohms

R_(3.4)=total resistance of stomach region/stomach fat in ohms.

Using the total capacitive reactance and total resistance of the stomachregion and stomach fat derived above, and assuming that the voltagebetween the electrodes is 1,000 volts, the current passing between theelectrodes through the stomach region and stomach fat is:

$\begin{matrix}{I = {\frac{1\text{,}000}{\sqrt{\left( {3\text{,}357.6} \right)^{2} + \left( {4\text{,916.06}} \right)^{2}}} = {0.168\mspace{14mu} {amps}}}} & (162)\end{matrix}$

Required Thickness of Acetic Acid

In order to obtain a substantially constant current across the chest andstomach regions of the body so that the same cell type in both regionsheats at substantially the same rate, the current passing between theelectrodes through the acetic acid and chest region (equation 146) mustbe equal to the current passing between the electrodes through thestomach region and stomach fat (equation 162), as follows:

$\begin{matrix}{0.168 = {\frac{1\text{,}000}{\sqrt{\left( {{1\text{,}996.4} + {2\text{,}857.6d_{1}}} \right)^{2} + \left( {{3\text{,}593.52} + {74.87d_{1}}} \right)^{2}}}\mspace{14mu} {amps}}} & (163)\end{matrix}$

By solving equation (163) for d₁, it can be seen that the requiredthickness of the acetic acid is 0.9429 inches. Thus, the compartments oftop bladder 68 adjacent the chest region (i.e., the row of compartmentslabeled 68 d) are filled with acetic acid having a thickness of 0.9429inches. In addition, the compartments of top bladder 68 adjacent thestomach region/stomach fat (i.e., the two rows of compartments labeled68 e and 68 f) are filled with a liquid conductor having a thickness of0.9429 inches to effectively narrow the spacing between the electrodesin this region.

Power and Change in Temperature

The power that is dissipated in the acetic acid due to the applicationof the dielectric field is expressed by the following equation:

P ₁ =R ₁ ×I ²  (164)

where

P₁=power in acetic acid in watts due to the dielectric field

R₁=resistance of acetic acid in ohms

I=current in amperes.

Using the resistance of the acetic acid and the current derived above,the power dissipated in the acetic acid due to the dielectric field is:

P ₁=(74.87×0.9429)×(0.168)²=1.99 watts  (165)

The increase in temperature of the acetic acid during the application ofthe dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{1}} = \frac{P_{1} \times t_{1}}{16.387\left( {h_{1} \times \rho_{1} \times d_{1}} \right)}} & (166)\end{matrix}$

where

ΔT₁=increase in temperature of acetic acid in ° C.

P₁=power in acetic acid in watts due to the dielectric field

t₁=heating time of acetic acid in seconds

h₁=specific heat of acetic acid in J/g ° C.

ρ₁=density of acetic acid in g/cm³

d₁=thickness of acetic acid in inches.

Using the power in the acetic acid derived above and assuming that thespecific heat and density of the acetic acid are 2.18 J/g ° C. and 1.05g/cm³, respectively, the increase in temperature of the acetic acidduring the application of the dielectric field is expressed as follows:

$\begin{matrix}{{\Delta \; T_{1}} = {\frac{1.99 \times t_{2}}{16.387\left( {2.18 \times 1.05 \times 0.9429} \right)} = {0.056 \times t_{1}\mspace{14mu} {^\circ}\mspace{14mu} {C.}}}} & (167)\end{matrix}$

Similarly, the power that is dissipated in the chest region due to theapplication of the dielectric field is expressed by the followingequation:

P ₂ =R ₂ ×I ²  (168)

where

P₂=power in chest region in watts due to the dielectric field

R₂=resistance of chest region in ohms

I=current in amperes.

Using the resistance of the chest region and the current derived above,the power dissipated in the chest region due to the dielectric field is:

P ₂=(3,593.52)×(0.168)²=101.42 watts  (169)

The increase in temperature of the chest region during the applicationof the dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{2}} = \frac{P_{2} \times t_{2}}{16.387\left( {h_{2} \times \rho_{2} \times d_{2}} \right)}} & (170)\end{matrix}$

where

ΔT₂=increase in temperature of chest region in ° C.

P₂=power in chest region in watts due to the dielectric field

t₂=heating time of chest region in seconds

h₂=specific heat of chest region in J/g ° C.

ρ₂=density of chest region in g/cm³

d₂=thickness of chest region in inches.

Using the power in the chest region derived above and assuming that thespecific heat and density of the chest region are 3.47 J/g ° C. and1.027 g/cm³, respectively, the increase in temperature of the chestregion during the application of the dielectric field is expressed asfollows:

$\begin{matrix}{{\Delta \; T_{2}} = {\frac{101.42 \times t_{2}}{16.387\left( {3.47 \times 1.027 \times 8} \right)} = {0.217 \times t_{2}\mspace{14mu} {^\circ}\mspace{14mu} {C.}}}} & (171)\end{matrix}$

Similarly, the power that is dissipated in the stomach region due to theapplication of the dielectric field is expressed by the followingequation:

P ₃ =R ₃ ×I ²  (172)

where

P₃=power in stomach region in watts due to the dielectric field

R₃=resistance of stomach region in ohms

I=current in amperes.

Using the resistance of the stomach region and the current derivedabove, the power dissipated in the stomach region due to the dielectricfield is:

P ₃=(3,144.06)×(0.168)²=88.74 watts  (173)

The increase in temperature of the stomach region during the applicationof the dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{3}} = \frac{P_{3} \times t_{2}}{16.387\left( {h_{3} \times \rho_{3} \times d_{3}} \right)}} & (174)\end{matrix}$

where

ΔT₃=increase in temperature of stomach region in ° C.

P₃=power in stomach region in watts due to the dielectric field

t₃=heating time of stomach region in seconds

h₃=specific heat of stomach region in J/g ° C.

ρ₃=density of stomach region in g/cm³

d₃=thickness of stomach region in inches.

Using the power in the stomach region derived above and assuming thatthe specific heat and density of the stomach region are 3.473 J/g° C.and 1.027 g/cm³, respectively, the increase in temperature of thestomach region during the application of the dielectric field isexpressed as follows:

$\begin{matrix}{{\Delta \; T_{3}} = {\frac{88.74 \times t_{3}}{16.387\left( {3.47 \times 1.027 \times 7} \right)} = {0.217 \times t_{3}\mspace{14mu} {^\circ}\mspace{14mu} {C.}}}} & (175)\end{matrix}$

Similarly, the power that is dissipated in the stomach fat due to theapplication of the dielectric field is expressed by the followingequation:

P ₄ =R ₄ ×I ²

where

P₄=power in stomach fat in watts due to the dielectric field

R₄=resistance of stomach fat in ohms

I=current in amperes.

Using the resistance of the stomach fat and the current derived above,the power dissipated in the stomach fat due to the dielectric field is:

P ₄=(1,772)×(0.168)²=50.01 watts  (177)

The increase in temperature of the stomach fat during the application ofthe dielectric field is represented by the following equation:

$\begin{matrix}{{\Delta \; T_{4}} = \frac{P_{4} \times t_{4}}{16.387\left( {h_{4} \times \rho_{4} \times d_{4}} \right)}} & (178)\end{matrix}$

where

ΔT₄=increase in temperature of stomach fat in ° C.

P₄=power in stomach fat in watts due to the dielectric field

t₄=heating time of stomach fat in seconds

h₄=specific heat of stomach fat in J/g ° C.

ρ₄=density of stomach fat in g/cm³

d₄=thickness of stomach fat in inches.

Using the power in the stomach fat derived above and assuming that thespecific heat and density of the stomach fat are 1.93 J/g° C. and 0.918g/cm³, respectively, the increase in temperature of the stomach fatduring the application of the dielectric field is expressed as follows:

$\begin{matrix}{{\Delta \; T_{4}} = {\frac{50.01 \times t_{4}}{16.387\left( {1.93 \times 0.918 \times 1} \right)} = {1.72 \times t_{4}\mspace{14mu} {^\circ}\mspace{14mu} {C.}}}} & (179)\end{matrix}$

Exemplary Change in Temperature After 15 Seconds

As set forth above, the increase in temperature of the acetic acid,chest region, stomach region and stomach fat during the application ofthe dielectric field are expressed as follows:

ΔT ₁=0.056×t ₁° C.  (180)

ΔT ₂=0.217×t ₂° C.  (181)

ΔT ₃=0.217×t ₃° C.  (182)

ΔT ₄=1.72×t ₄° C.  (183)

If, for example, the heating time is 15 seconds (i.e., the human body isexposed to the dielectric field for 15 seconds), the increase intemperature of the acetic acid is 0.843° C. (or 1.5° F.), the increasein temperature of the chest and stomach regions is 3.256° C. (or 5.86°F.), and the increase in temperature of the stomach fat is. 25.8° C. (or46.44° F.). Thus, if the human body starts at 98.6° F. (i.e., bodytemperature) and the acetic acid starts at 77° F., then the temperaturesof the acetic acid, chest and stomach regions and stomach fat are 78.5°F., 104.46° F. and 145° F., respectively, at the end of the dielectricheating treatment.

In this example, it can be seen that the chest and stomach regions heatat the same rate. The stomach fat heats at a much faster rate and willliquefy during the dielectric heating treatment. Preferably, theliquefied stomach fat is removed from the body through any means knownin the art (e.g., syringe or liposuction). It can also be seen that thetemperature of the acetic acid is relatively low at the end of thedielectric heating treatment (i.e., 78.5° F.). Accordingly, the aceticacid does not heat the skin of the human body during the dielectricheating treatment and also serves to cool the body upon completion ofthe dielectric heating treatment. Further, the acetic, acid may beChilled prior to, during and/or after the dielectric heating treatmentso as to provide an even greater cooling effect on the human body.

IV. Dielectric Heating of Biological Targets of a Subject

As discussed in Section III above, the apparatuses and methods of thepresent invention enable a substantially constant current to be obtainedacross a treatment region of a subject when subjected to a dielectricfield. If the current is substantially constant, then the ratio of thechange in temperature of the biological targets (e.g., target cells) tothe change in temperature of the non-targets (e.g., non-target cells) isdependent on the dissipation factor, dielectric constant, specific heatand density of the cell types, as follows:

$\begin{matrix}{\frac{\Delta \; T_{2}}{\Delta \; T_{1}} = \frac{{df}_{2} \times ɛ_{1} \times h_{1} \times \rho_{1}}{{df}_{1} \times ɛ_{2} \times h_{2} \times \rho_{2}}} & (184)\end{matrix}$

where

ΔT₁=increase in temperature of non-target cells in ° C.

ΔT₂=increase in temperature of target cells in ° C.

df₁=dissipation factor of non-target cells

df₂=dissipation factor of target cells

∈₁=dielectric constant of non-target cells

∈₂=dielectric constant of target cells

h₁=specific heat of non-target cells in J/g° C.

h₂=specific heat of target cells in J/g° C.

ρ₁=density of non-target cells in g/cm³

ρ₂=density of target cells in g/cm³.

As such, if it is desired to heat the target cells X times faster thanthe non-target cells, then this ratio must be X. In some cases, theratio of X occurs naturally. In other cases, the ratio of X is achievedby introducing a dielectric heating modulator into the subject that willbind to the target cells (as described above) in a percentage sufficientto raise the temperature of the target cells to a temperature where thetarget cells will be killed, without damaging the non-target cells.

It should be understood that the dissipation factor, dielectricconstant, specific heat, and density of the non-target cells and targetcells vary with temperature. Therefore, it is preferable to calculatethe ratio in equation (184) at regular time intervals (e.g., 1 secondtime intervals). By doing so, it is possible to use the values for thedissipation factor, dielectric constant, specific heat, and density thatcorrespond to the temperature of the non-target cells and target cellsat that particular point in time. Preferably, a computer is programmedto perform these calculations in order to simplify the analysis.

It should also be understood that equation (184) does not consider theeffects of thermal conductivity on the temperatures of the non-targetcells and target cells at the end of the dielectric heating treatment.In general, it is preferable to utilize a short heating time so as tominimize the effects of thermal conductivity between the non-targetcells and target cells (which can be accomplished, for example, by usinga higher voltage). A longer heating time has two disadvantages: (1) allor a portion of the non-target cells surrounding the target cells may beheated by thermal conductivity so as to kill the non-target cells; and(2) if a small number of target cells are surrounded by a larger numberof non-target cells, the non-target cells may cool the target cells bythermal conductivity to a point where the target cells will not bekilled. Thus, if a longer heating time is utilized for a particularapplication, it is necessary to consider the effects of thermalconductivity on the temperatures of the non-target cells and targetcells at the end of the dielectric heating treatment. Accordingly, ashort heating time is preferred.

It should further be understood that the application of equation (184)is not limited to a treatment region that includes target cells and asingle type of non-target cells. Indeed, equation (184) can be appliedto a treatment region that includes any number of cell types. Forexample, if a treatment region includes n different types of non-targetcells, it is only necessary to focus on the non-target cell type thatheats at the fastest rate. If the non-target cell type that heats at thefastest rate is not killed, then none of the other non-target cell typeswill be killed by the dielectric heating. In order to demonstrate thisprinciple, the derivation of equation (184) is provided below for casesin which (1) a treatment region includes two different cell types and(2) a treatment region includes six different cell types.

Two Cell Types

In this analysis, it is assumed that the treatment region includes afirst type of non-target cells and a second type of target cells,wherein the subscripts 1 and 2 are used to denote each of these celltypes.

The capacitance of the non-target cells is expressed by the followingequation:

$\begin{matrix}{C_{1} = \frac{ɛ_{1} \times A \times 0.2249}{d_{1}}} & (185)\end{matrix}$

where

C₁=capacitance of non-target cells in picofarads

∈₁=dielectric constant of non-target cells

A=area of non-target cells in inches²

d₁=thickness of non-target cells in inches.

Similarly, the capacitance of the target cells is expressed by thefollowing equation:

$\begin{matrix}{C_{2} = \frac{ɛ_{2} \times A \times 0.2249}{d_{2}}} & (186)\end{matrix}$

where

C₂=capacitance of target cells in picofarads

∈₂=dielectric constant of target cells

A=area of target cells in inches²

d₂=thickness of target cells in inches.

The capacitive reactance of the non-target cells is given by thefollowing equation:

$\begin{matrix}{X_{{C\; 1}\;} = \frac{1}{2 \times \pi \times f \times C_{1}}} & (187)\end{matrix}$

where

X_(C1)=capacitive reactance of non-target cells in ohms

f=frequency of dielectric field in hertz

C₁=capacitance of non-target cells in farads.

Using the capacitance of the non-target cells derived above, thecapacitive reactance of the non-target cells is:

$\begin{matrix}{X_{C\; 1} = {\frac{d_{1}}{2 \times \pi \times f \times ɛ_{1} \times A \times 0.2249 \times 10^{- 12}}\mspace{14mu} {ohms}}} & (188)\end{matrix}$

Similarly, the capacitive reactance of the target cells is given by thefollowing equation:

$\begin{matrix}{X_{C\; 2} = \frac{1}{2 \times \pi \times f \times C_{2}}} & (189)\end{matrix}$

where

X_(C2)=capacitive reactance of target cells in ohms

f=frequency of dielectric field in hertz

C₂=capacitance of target cells in farads.

Using the capacitance of the target cells derived above, the capacitivereactance of the target cells is:

$\begin{matrix}{X_{C\; 2} = {\frac{d_{2}}{2 \times \pi \times f \times ɛ_{2} \times A \times 0.2249 \times 10^{- 12}}\mspace{14mu} {ohms}}} & (190)\end{matrix}$

Then, the total capacitive reactance of the non-target cells and thetarget cells is obtained by adding equations (188) and (190), asfollows:

$\begin{matrix}{X_{C} = {\frac{{ɛ_{1}d_{2}} + {ɛ_{2}d_{1}}}{ɛ_{1} \times ɛ_{2} \times 2 \times \pi \times f \times A \times 0.2249 \times 10^{- 12}}\mspace{14mu} {ohms}}} & (191)\end{matrix}$

The resistance of the non-target cells is equal to the product of thedissipation factor of the non-target cells and the capacitive reactanceof the non-target cells, as follows:

R ₁ =df ₁ ×X _(C1)

where

R₁=resistance of non-target cells in ohms

df₁=dissipation factor of non-target cells

X_(C1)=capacitive reactance of non-target cells in ohms.

Using the capacitive reactance of the non-target cells derived above,the resistance of the non-target cells is:

$\begin{matrix}{R_{1} = {\frac{{df}_{1} \times d_{1}}{ɛ_{1} \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12}}\mspace{14mu} {ohms}}} & (193)\end{matrix}$

Similarly, the resistance of the target cells is equal to the product ofthe dissipation factor of the target cells and the capacitive reactanceof the target cells, as follows:

R ₂ =df ₂ ×X _(C2)  (194)

where

R₂=resistance of target cells in ohms

df₂=dissipation factor of target cells

X_(C2)=capacitive reactance of target cells in ohms.

Using the capacitive reactance of the target cells derived above, theresistance of the target cells is:

$\begin{matrix}{R_{2} = {\frac{{df}_{2} \times d_{2}}{ɛ_{2} \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12}}\mspace{14mu} {ohms}}} & (195)\end{matrix}$

Then, the total resistance of the non-target cells and the target cellsis obtained by adding equations (193) and (195), as follows:

$\begin{matrix}{R = {\frac{1}{A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12}}\left( {\frac{{df}_{1} \times d_{1}}{ɛ_{1}} + \frac{{df}_{2} \times d_{2}}{ɛ_{2}}} \right)\mspace{14mu} {ohms}}} & (196)\end{matrix}$

The current passing between the electrodes through the non-target cellsand the target cells is represented by the following equation:

$\begin{matrix}{I = \frac{V}{\sqrt{X_{C}^{2} + R^{2}}}} & (197)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts.

X_(C)=total capacitive reactance of non-target and target cells in ohms

R=total resistance of non-target and target cells in ohms.

Using the total capacitive reactance and total resistance of thenon-target cells and the target cells derived above, the current passingbetween the electrodes through the non-target cells and the target cellsis:

$\begin{matrix}{I = \frac{V \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12} \times ɛ_{1} \times ɛ_{2}}{\sqrt{\left( {{ɛ_{1}d_{2}} + {ɛ_{2}d_{1}}} \right)^{2} + \left( {{{df}_{1}d_{1}ɛ_{2}} + {{df}_{2}d_{2}ɛ_{1}}} \right)^{2}}}} & (198)\end{matrix}$

The power that is dissipated in the non-target cells due to theapplication of the dielectric field is expressed by the followingequation:

P ₁ =R ₁ ×I ²  (199)

where

P₁=power in non-target cells in watts due to the dielectric field

R₁=resistance of non-target cells in ohms

I=current in amperes.

Using the resistance of the non-target cells and current derived above,the power dissipated in the non-target cells due to the dielectric fieldis:

$\begin{matrix}{P_{1} = \frac{{df}_{1} \times d_{1} \times V^{2} \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12} \times ɛ_{1} \times ɛ_{2}^{2}}{\left( {{ɛ_{1}d_{2}} + {ɛ_{2}d_{1}}} \right)^{2} + \left( {{{df}_{1}d_{1}ɛ_{2}} + {{df}_{2}d_{2}ɛ_{1}}} \right)^{2}}} & (200)\end{matrix}$

Similarly, the power that is dissipated in the target cells due to theapplication of the dielectric field is expressed by the followingequation:

P ₂ =R ₂ ×I ²  (201)

where

P₂=power in target cells in watts due to the dielectric field

R₂=resistance of target cells in ohms

I=current in amperes.

Using the resistance of the target cells and current derived above, thepower dissipated in the target cells, due to the dielectric field is:

$\begin{matrix}{P_{2} = \frac{{df}_{2} \times d_{2} \times V^{2} \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12} \times ɛ_{2} \times ɛ_{1}^{2}}{\left( {{ɛ_{2}d_{1}} + {ɛ_{1}d_{2}}} \right)^{2} + \left( {{{df}_{2}d_{2}ɛ_{1}} + {{df}_{1}d_{1}ɛ_{2}}} \right)^{2}}} & (202)\end{matrix}$

The increase in temperature of the non-target cells during theapplication of the dielectric field is represented by the followingequation:

$\begin{matrix}{{\Delta \; T_{1}} = \frac{P_{1} \times t_{1}}{16.387\; \left( {h_{1} \times \rho_{1} \times d_{1}} \right)}} & (203)\end{matrix}$

where

ΔT₁=increase in temperature of non-target cells in ° C.

P₁=power in non-target cells in watts due to the dielectric field

t₁=heating time of non-target cells in seconds

h₁=specific heat of non-target cells in J/g° C.

ρ₁=density of non-target cells in g/cm³

d₁=thickness of non-target cells in inches.

Using the power in the non-target cells derived above, the increase intemperature of the non-target cells during the application of thedielectric field is:

$\begin{matrix}{{\Delta \; T_{1}} = \frac{{df}_{1} \times V^{2} \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12} \times ɛ_{1} \times ɛ_{2}^{2} \times t_{1}}{16.387 \times h_{1} \times {\rho_{1}\left( {\left( {{ɛ_{1}d_{2}} + {ɛ_{2}d_{1}}} \right)^{2} + \left( {{{df}_{1}d_{1}ɛ_{2}} + {{df}_{2}d_{2}ɛ_{1}}} \right)^{2}} \right)}}} & (204)\end{matrix}$

Similarly, the increase in temperature of the target cells during theapplication of the dielectric field is represented by the followingequation:

$\begin{matrix}{{\Delta \; T_{2}} = \frac{P_{2} \times t_{2}}{16.387\left( {h_{2} \times \rho_{2} \times d_{2}} \right)}} & (205)\end{matrix}$

where

ΔT₂=increase in temperature of target cells in ° C.

P₂=power in target cells in watts due to the dielectric field

t₂=heating time of target cells in seconds

h₂=specific heat of target cells in J/g ° C.

ρ₂=density of target cells in g/cm³

d₂=thickness of target cells in inches.

Using the power in the target cells derived above, the increase intemperature of the target cells during the application of the dielectricfield is:

$\begin{matrix}{{\Delta \; T_{2}} = \frac{{df}_{2} \times V^{2} \times A \times 2 \times \pi \times f \times 0.2249 \times 10^{- 12} \times ɛ_{2} \times ɛ_{1}^{2} \times t_{2}}{16.387 \times h_{2} \times {\rho_{2}\left( {\left( {{ɛ_{2}d_{1}} + {ɛ_{1}d_{2}}} \right)^{2} + \left( {{{df}_{2}d_{2}ɛ_{1}} + {{df}_{1}d_{1}ɛ_{2}}} \right)^{2}} \right)}}} & (206)\end{matrix}$

The ratio of the change in temperature of the target cells to the changein temperature of the non-target cells is then expressed by dividingequations (206) and (204), as follows:

$\begin{matrix}{\frac{{\Delta T}_{2}}{\Delta \; T_{1}} = \frac{{df}_{2} \times ɛ_{1} \times h_{1} \times \rho_{1}}{{df}_{1} \times ɛ_{2} \times h_{2} \times \rho_{2}}} & (207)\end{matrix}$

Thus, it can be seen that equation (207) is the same as equation (184)set forth above.

Six Cell Types

The analysis set forth above becomes more complex as additional celltypes are included in the treatment region. In the following analysis,it is assumed that the treatment region includes five different types ofnon-target cells and a sixth type of target cells, wherein thesubscripts 1-6 are used to denote each of these cell types.

The capacitance of each of the cell types is expressed by the followingequation:

$\begin{matrix}{C_{i} = \frac{ɛ_{i} \times A \times 0.2249}{d_{i}}} & (208)\end{matrix}$

where

C_(i)=capacitance of cell type in picofarads

∈_(i)=dielectric constant of cell type

A=area of cell type in inches²

d_(i)=thickness of cell type in inches.

Looking at the same area A of 1 inch² for each of the six cell types,the capacitance of each of the cell types is expressed as follows:

$\begin{matrix}{C_{1} = {\frac{ɛ_{1} \times 0.2249}{d_{1}}\mspace{14mu} {pF}}} & (209) \\{C_{2} = {\frac{ɛ_{2} \times 0.2249}{d_{2}}\mspace{14mu} {pF}}} & (210) \\{C_{3} = {\frac{ɛ_{3} \times 0.2249}{d_{3}}\mspace{14mu} {pF}}} & (211) \\{C_{4} = {\frac{ɛ_{4} \times 0.2249}{d_{4}}\mspace{14mu} {pF}}} & (212) \\{C_{5} = {\frac{ɛ_{5} \times 0.2249}{d_{5}}\mspace{14mu} {pF}}} & (213) \\{C_{6} = {\frac{ɛ_{6} \times 0.2249}{d_{6}}\mspace{14mu} {pF}}} & (214)\end{matrix}$

The total capacitance of all six cell types is represented by thefollowing equation:

$\begin{matrix}{C = \frac{C_{1} \times C_{2} \times C_{3} \times C_{4} \times C_{5} \times C_{6}}{\begin{matrix}{{C_{1}C_{2}C_{3}C_{4}C_{5}} + {C_{1}C_{2}C_{3}C_{4}C_{6}} + {C_{1}C_{2}C_{3}C_{5}C_{6}} +} \\{{C_{1}C_{2}C_{4}C_{5}C_{6}} + {C_{1}C_{3}C_{4}C_{5}C_{6}} + {C_{2}C_{3}C_{4}C_{5}C_{6}}}\end{matrix}}} & (215)\end{matrix}$

where

C=equivalent capacitance of six cell types in picofarads

C₁=capacitance of cell type 1 in picofarads

C₂=capacitance of cell type 2 in picofarads

C₃=capacitance of cell type 3 in picofarads

C₄=capacitance of cell type 4 in picofarads

C₅=capacitance of cell type 5 in picofarads

C₆=capacitance of cell type 6 in picofarads.

Using the capacitance of each of the cell types derived above, the totalcapacitance is:

$\begin{matrix}{C = \frac{\left( {{.2249} \times 10^{- 12}\left( {\frac{ɛ_{1}}{d_{1}} \times \frac{ɛ_{2}}{d_{2}} \times \frac{ɛ_{3}}{d_{3}} \times \frac{ɛ_{4}}{d_{4}} \times \frac{ɛ_{5}}{d_{5}} \times \frac{ɛ_{6}}{d_{6}}} \right)} \right)}{\begin{matrix}{\frac{ɛ_{1} \times ɛ_{2} \times ɛ_{3} \times ɛ_{4} \times ɛ_{5}}{d_{1} \times d_{2} \times d_{3} \times d_{4} \times d_{5}} + \frac{ɛ_{1} \times ɛ_{2} \times ɛ_{3} \times ɛ_{4} \times ɛ_{6}}{d_{1} \times d_{2} \times d_{3} \times d_{4} \times d_{6}} + \frac{ɛ_{1} \times ɛ_{2} \times ɛ_{3} \times ɛ_{5} \times ɛ_{6}}{d_{1} \times d_{2} \times d_{3} \times d_{5} \times d_{6}} +} \\{\frac{ɛ_{1} \times ɛ_{2} \times ɛ_{4} \times ɛ_{5} \times ɛ_{6}}{d_{1} \times d_{2} \times d_{4} \times d_{5} \times d_{6}} + \frac{ɛ_{1} \times ɛ_{3} \times ɛ_{4} \times ɛ_{5} \times ɛ_{6}}{d_{1} \times d_{3} \times d_{4} \times d_{5} \times d_{6}} + \frac{ɛ_{2} \times ɛ_{3} \times ɛ_{4} \times ɛ_{5} \times ɛ_{6}}{d_{2} \times d_{3} \times d_{4} \times d_{5} \times d_{6}}}\end{matrix}}} & (216)\end{matrix}$

The capacitive reactance of each of the cell types is given by thefollowing equation:

$\begin{matrix}{X_{Ci} = \frac{1}{2 \times \pi \times f \times C_{i}}} & (217)\end{matrix}$

where

X_(Ci)=capacitive reactance of cell type in ohms

f=frequency of dielectric field in hertz

C_(i)=capacitance of cell type in farads.

Using the capacitance of each of the cell types derived above andassuming that the frequency of the dielectric field is 40 MHz, thecapacitive reactance of each of the cell types is expressed as follows:

$\begin{matrix}{X_{C\; 1} = {\frac{17\text{,}716 \times d_{1}}{ɛ_{1}}\mspace{14mu} {ohms}}} & (218) \\{X_{C\; 2} = {\frac{17\text{,}716 \times d_{2}}{ɛ_{2\;}}\mspace{14mu} {ohms}}} & (219) \\{X_{C\; 3} = {\frac{17\text{,}716 \times d_{3}}{ɛ_{3\;}}\mspace{14mu} {ohms}}} & (220) \\{X_{C\; 4} = {\frac{17\text{,}716 \times d_{4}}{ɛ_{4}}\mspace{14mu} {ohms}}} & (221) \\{X_{C\; 5} = {\frac{17\text{,}716 \times d_{5}}{ɛ_{5}}\mspace{14mu} {ohms}}} & (222) \\{X_{C\; 6} = {\frac{17\text{,}716 \times d_{6}}{ɛ_{6}}\mspace{14mu} {ohms}}} & (223)\end{matrix}$

Also, the total capacitive reactance of all six cell types is given bythe following equation:

$\begin{matrix}{X_{C} = \frac{1}{2 \times \pi \times f \times C}} & (224)\end{matrix}$

where

X_(C)=total capacitive reactance of six cell types in ohms

f=frequency of dielectric field in hertz

C=total capacitance of six cell types in farads.

Using the total capacitance of all six cell types derived above andassuming that the frequency of the dielectric field is 40 MHz, the totalcapacitive reactance of the six cell types is expressed as follows:

$\begin{matrix}{X_{C} = \frac{17\text{,}716\begin{pmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{\frac{ɛ_{1} \times ɛ_{2} \times ɛ_{3} \times ɛ_{4} \times ɛ_{5}}{d_{1} \times d_{2} \times d_{3} \times d_{4} \times d_{5}} +} \\{\frac{ɛ_{1} \times ɛ_{2} \times ɛ_{3} \times ɛ_{4} \times ɛ_{6}}{d_{1} \times d_{2} \times d_{3} \times d_{4} \times d_{6}} +}\end{matrix} \\{\frac{ɛ_{1} \times ɛ_{2} \times ɛ_{3} \times ɛ_{5} \times ɛ_{6}}{d_{1} \times d_{2} \times d_{3\;} \times d_{5} \times d_{6}} +}\end{matrix} \\{\frac{ɛ_{1} \times ɛ_{2} \times ɛ_{4} \times ɛ_{5} \times ɛ_{6}}{d_{1} \times d_{2} \times d_{4} \times d_{5} \times d_{6}} +}\end{matrix} \\{\frac{ɛ_{1} \times ɛ_{3} \times ɛ_{4} \times ɛ_{5} \times ɛ_{6}}{d_{1} \times d_{3} \times d_{4} \times d_{5} \times d_{6\;}} +}\end{matrix} \\\frac{ɛ_{2} \times ɛ_{3} \times ɛ_{4} \times ɛ_{5} \times ɛ_{6}}{d_{2} \times d_{3} \times d_{4} \times d_{5} \times d_{6}}\end{pmatrix}}{\left( {\frac{ɛ_{1}}{d_{1}} \times \frac{ɛ_{2}}{d_{2}} \times \frac{ɛ_{3}}{d_{3}} \times \frac{ɛ_{4}}{d_{4}} \times \frac{ɛ_{5}}{d_{5}} \times \frac{ɛ_{6}}{d_{6}}} \right)}} & (225)\end{matrix}$

The resistance of each of the cell types is equal to the product of thedissipation factor of the cell type and the capacitive reactance of thecell type, as follows:

R _(i) =df _(i) ×X _(Ci)  (226)

where

R_(i)=resistance of cell type in ohms

df_(i)=dissipation factor of cell type.

X_(Ci)=capacitive reactance of cell type in ohms.

Using the capacitive reactance of each of the cell types derived above,the resistance of each of the cell types is:

$\begin{matrix}{R_{1} = {\frac{17\text{,}716 \times {df}_{1} \times d_{1}}{ɛ_{1}}\mspace{14mu} {ohms}}} & (227) \\{R_{2} = {\frac{17\text{,}716 \times {df}_{2} \times d_{2}}{ɛ_{2}}\mspace{14mu} {ohms}}} & (228) \\{R_{3} = {\frac{17\text{,}716 \times {df}_{3} \times d_{3}}{ɛ_{3}}\mspace{14mu} {ohms}}} & (229) \\{R_{4} = {\frac{17\text{,}716 \times {df}_{4} \times d_{4}}{ɛ_{4}}\mspace{14mu} {ohms}}} & (230) \\{R_{5} = {\frac{17\text{,}716 \times d_{5} \times d_{5}}{ɛ_{5}}\mspace{14mu} {ohms}}} & (231) \\{R_{6} = {\frac{17\text{,}716 \times {df}_{6} \times d_{6}}{ɛ_{6}}\mspace{14mu} {ohms}}} & (232)\end{matrix}$

Then, the total resistance of all six cell types is obtained by addingequations (227) to (232), as follows.

$\begin{matrix}{R = {17\text{,}716\left( {\frac{{df}_{1}d_{1}}{ɛ_{1}} + \frac{{df}_{2}d_{2}}{ɛ_{2\;}} + \frac{{df}_{3}d_{3}}{ɛ_{3}} + \frac{{{df}_{4}d_{4}}\;}{ɛ_{4}} + \frac{{df}_{5}d_{5}}{ɛ_{5}} + \frac{{df}_{6}d_{6}}{ɛ_{6\;}}} \right)}} & (233)\end{matrix}$

The current passing between the electrodes through the six cell types isrepresented by the following equation:

$\begin{matrix}{I = \frac{V}{\sqrt{X_{C}^{2} + R^{2}}}} & (234)\end{matrix}$

where

I=current in amperes

V=voltage between the electrodes in volts

X_(C)=total capacitive reactance of six cell types in ohms

R=total resistance of six cell types in ohms.

Using the total capacitive reactance and total resistance of the sixcell types derived above, the current passing between the six cell typesis:

$\begin{matrix}{I = \frac{V \times 56.44 \times 10^{- 6} \times ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{4}ɛ_{5}ɛ_{6}}{\sqrt{\begin{matrix}{\begin{pmatrix}\begin{matrix}\begin{matrix}{{ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{4}ɛ_{5}d_{6}} +} \\{{ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{4}ɛ_{6}d_{5}} +}\end{matrix} \\{{ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{5}ɛ_{6}d_{4}} +}\end{matrix} \\{{ɛ_{1}ɛ_{2}ɛ_{4}ɛ_{5}ɛ_{6}d_{3}} +} \\{{ɛ_{1}ɛ_{3}ɛ_{4}ɛ_{5}ɛ_{6}d_{2}} +} \\{ɛ_{2}ɛ_{3}ɛ_{4}ɛ_{5}ɛ_{6}d_{1}}\end{pmatrix}^{2} +} \\\begin{pmatrix}\begin{matrix}{{{df}_{1}d_{1}ɛ_{1}ɛ_{3}ɛ_{4}ɛ_{5}ɛ_{6}} +} \\{{{df}_{2}d_{2}ɛ_{1}ɛ_{3}ɛ_{4}ɛ_{5}ɛ_{6}} +}\end{matrix} \\{{{df}_{3}d_{3}ɛ_{1}ɛ_{2}ɛ_{4}ɛ_{5}ɛ_{6}} +} \\{{{df}_{4}d_{4}ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{5}ɛ_{6}} +} \\{{{df}_{5}d_{5}ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{4}ɛ_{6}} +} \\{{df}_{6}d_{6}ɛ_{1}ɛ_{2}ɛ_{3}ɛ_{4}ɛ_{5}}\end{pmatrix}^{2}\end{matrix}}}} & (235)\end{matrix}$

The power that is dissipated in each of the six cell types due to theapplication of the dielectric field is expressed by the followingequation:

P _(i) =R _(i) ×I ²  (236)

where

P_(i)=power in cell type in watts due to the dielectric field

R_(i)=resistance of cell type in ohms

I=current in amperes.

Using the resistance of each cell type derived above, the powerdissipated in each cell type due to the electric field is expressed as:

$\begin{matrix}{P_{1} = {\frac{17\text{,}716 \times {df}_{1} \times d_{1} \times I^{2}}{ɛ_{1}} = {\frac{{df}_{1} \times d_{1}}{ɛ_{1}} \times k\; 1}}} & (237) \\{P_{2} = {\frac{17\text{,}716 \times {df}_{2} \times d_{2} \times I^{2}}{ɛ_{2}} = {\frac{{df}_{2} \times d_{2}}{ɛ_{2}} \times k\; 1}}} & (238) \\{P_{3} = {\frac{17\text{,}716 \times {df}_{3} \times d_{3} \times I^{2}}{ɛ_{3}} = {\frac{{df}_{3} \times d_{3}}{ɛ_{3}} \times k\; 1}}} & (239) \\{P_{4} = {\frac{17\text{,}716 \times {df}_{4} \times d_{4} \times I^{2}}{ɛ_{4}} = {\frac{{df}_{4} \times d_{4}}{ɛ_{4}} \times k\; 1}}} & (240) \\{P_{5} = {\frac{17\text{,}716 \times {df}_{5} \times d_{5} \times I^{2}}{ɛ_{5}} = {\frac{{df}_{5} \times d_{5}}{ɛ_{5}} \times k\; 1}}} & (241) \\{P_{6} = {\frac{17\text{,}716 \times {df}_{6} \times d_{6} \times I^{2}}{ɛ_{6}} = {\frac{{df}_{6} \times d_{6}}{ɛ_{6}} \times k\; 1}}} & (242)\end{matrix}$

It should be understood that the constant k1 (i.e., 17,716×I²) is thesame for each of equations (237) to (242).

The increase in temperature of each of the cell types during theapplication of the dielectric field is represented by the followingequation:

$\begin{matrix}{{\Delta \; T_{i}} = \frac{P_{i} \times t}{16.387\left( {h_{i} \times \rho_{i} \times d_{i}} \right)}} & (243)\end{matrix}$

where

ΔT_(i)=increase in temperature of cell type in ° C.

P_(i)=power in cell type in watts due to the dielectric field,

t=heating time of cell type in seconds.

h_(i)=specific heat of cell type in J/g° C.

ρ_(i)=specific gravity of cell type in g/cm³

d_(i)=thickness of cell type in inches.

Using the power in each cell type derived above, the increase intemperature of each cell type during the application of the dielectricfield is expressed as follows:

$\begin{matrix}{{\Delta \; T_{1}} = {\frac{{df}_{1} \times d_{1} \times k\; 1 \times t}{ɛ_{1} \times 16.387 \times h_{1} \times \rho_{1} \times d_{1}} = {\frac{{df}_{1}}{ɛ_{1} \times h_{1} \times \rho_{1}} \times k\; 2 \times t}}} & (244) \\{{\Delta \; T_{2}} = {\frac{{df}_{2} \times d_{2} \times k\; 1 \times t}{ɛ_{2} \times 16.387 \times h_{2} \times \rho_{2} \times d_{2}} = {\frac{{df}_{2}}{ɛ_{2} \times h_{2} \times \rho_{2}} \times k\; 2 \times t}}} & (245) \\{{\Delta \; T_{3}} = {\frac{{df}_{3} \times d_{3} \times k\; 1 \times t}{ɛ_{3} \times 16.387 \times h_{3} \times \rho_{3} \times d_{3}} = {\frac{{df}_{3}}{ɛ_{3} \times h_{3} \times \rho_{3}} \times k\; 2 \times t}}} & (246) \\{{\Delta \; T_{4}} = {\frac{{df}_{4} \times d_{4} \times k\; 1 \times t}{ɛ_{4} \times 16.387 \times h_{4} \times \rho_{4} \times d_{4}} = {\frac{{df}_{4}}{ɛ_{4} \times h_{4} \times \rho_{4}} \times k\; 2 \times t}}} & (247) \\{{\Delta \; T_{5}} = {\frac{{df}_{5} \times d_{5} \times k\; 1 \times t}{ɛ_{5} \times 16.387 \times h_{5} \times \rho_{5} \times d_{5}} = {\frac{{df}_{5}}{ɛ_{5} \times h_{5} \times \rho_{5}} \times k\; 2 \times t}}} & (248) \\{{\Delta \; T_{6}} = {\frac{{df}_{6} \times d_{6} \times k\; 1 \times t}{ɛ_{6} \times 16.387 \times h_{6} \times \rho_{6} \times d_{6}} = {\frac{{df}_{6}}{ɛ_{6} \times h_{6} \times \rho_{6}} \times k\; 2 \times t}}} & (249)\end{matrix}$

It should be understood that the constant k2 (i.e., k1/16.387) is thesame for each of equations (244) to (249).

The ratio of the change in temperature of the target cells to the changein temperature of each of the non-target cells is then expressed bydividing equation (249) and each of equations (244) through (248), asfollows:

$\begin{matrix}{\frac{\Delta \; T_{6}}{\Delta \; T_{1}} = \frac{{df}_{6} \times ɛ_{1} \times h_{1} \times \rho_{1}}{{df}_{1} \times ɛ_{6} \times h_{6} \times \rho_{6}}} & (250) \\{\frac{\Delta \; T_{6}}{\Delta \; T_{2}} = \frac{{df}_{6} \times ɛ_{2} \times h_{2} \times \rho_{2}}{{df}_{2} \times ɛ_{6} \times h_{6} \times \rho_{6}}} & (251) \\{\frac{\Delta \; T_{6}}{\Delta \; T_{3\;}} = \frac{{df}_{6} \times ɛ_{3} \times h_{3} \times \rho_{3}}{{df}_{3} \times ɛ_{6} \times h_{6} \times \rho_{6}}} & (252) \\{\frac{\Delta \; T_{6}}{\Delta \; T_{4}} = \frac{{df}_{6} \times ɛ_{4} \times h_{4} \times \rho_{4}}{{df}_{4} \times ɛ_{6} \times h_{6} \times \rho_{6}}} & (253) \\{\frac{\Delta \; T_{6}}{\Delta \; T_{5}} = \frac{{df}_{6} \times ɛ_{5} \times h_{5} \times \rho_{5}}{{df}_{5} \times ɛ_{6} \times h_{6} \times \rho_{6\mspace{11mu}}}} & (254)\end{matrix}$

Thus, it can be seen that each of equations (250) through (254) is thesame as equation (184) set forth above. As discussed above, even thoughthe treatment region includes five different types of non-target cellsin this example, it is only necessary to focus on the non-target celltype that heats at the fastest rate. If the non-target cell type thatheats at the fastest rate is not killed, then none of the othernon-target cell types will be killed by the dielectric heating.

As an example, the dielectric constant, dissipation factor, specificheat and density of various cell types are summarized in the table below(assuming that the same amount of current is passing between each organor cell type), wherein the power and change of temperature arecalculated using the equations set forth above:

Dissi- Dielectric pation Specific Change of Constant Factor Heat DensityPower Temperature Blood 71 2.1 3.816 1.055 1.012 0.896 × t Brain 73.51.98 3.68 1.035 0.922 0.863 × t Bone 23 0.45 1.26 2.1 0.670 0.902 × tKidney 80.5 2.05 3.89 1.05 0.871 0.760 × t Spleen 77 2.25 3.816 1.0541.000 0.886 × t Liver 73.5 1.65 3.411 1.06 0.768 0.757 × t Muscle 772.25 3.47 1.027 1.000 1.000 × t Fat 11 1.1 1.93 0.918 3.422 6.883 × t

It can be seen that fat will heat at the fastest rate, followed bymuscle, bone, blood, spleen, brain, kidney and liver. Thus, if atreatment region contains a substantial amount of fat, then the adiposecell type would be considered in equation (184) in relation to thetarget cells. However, if a treatment region does not contain asubstantial amount of fat, then the muscle cell type would be consideredin equation (184) in relation to the target cells (or the cell type withthe fastest heating rate that is contained within the treatment-region).Of course, it may be desirable to eliminate adipose cells in a treatmentregion such that the cell type with the next fastest heating rate wouldbe considered in equation (184) in relation to the target cells.

A. Target Cells Naturally Heat at Faster Rate Relative to Non-TargetCells

In cases where the target cells and non-target cells have dissimilardielectric constants, dissipation factors, specific heats, anddensities, or combinations thereof, the target, cells and non-targetcells naturally heat at different rates. For example, it is estimatedthat many cells in the human body have a dielectric constant of about71, a dissipation factor of about 1.8, a specific heat of about 3.47J/g° C., and a density of about 1.027 g/cm³ when placed in a dielectricfield having a frequency of 40 MHz. In contrast, adipose cells (whichcontain large amounts of fat) have a dielectric constant of about 11, adissipation factor of about 1.1, a specific heat, of about 1.93 J/g° C.,and a density of about 0.918 g/cm³ when placed in a dielectric fieldhaving a frequency of 40 MHz. Using these values in equation (184), theratio of the change in temperature of the adipose cells (i.e., thetarget cells) to the change in temperature of the other cells in thehuman body (i.e., the non-target cells) is expressed by the followingequation:

$\begin{matrix}{\frac{\Delta \; T_{{adipose}\mspace{14mu} {cells}}}{\Delta \; T_{{other}\mspace{14mu} {cells}}} = {\frac{1.1 \times 71 \times 3.47 \times 1.027}{1.8 \times 11 \times 1.93 \times 0.918} = 7.93}} & (255)\end{matrix}$

As such, adipose cells naturally heat approximately 7.93 times fasterthan the other cells in the human body upon application of thedielectric field. Thus, the adipose cells reach higher temperatures thanthe other cells in the human body at the end of the dielectric heatingtreatment such that the adipose cells may be selectively killed comparedto non-adipose cell types that heat at much lower rates. Of course, itshould be understood that the dissipation factor, dielectric constant,specific heat, and density of the adipose cells and the other cells inthe human body vary with temperature. As such, it would be preferable tocalculate the ratio in equation (184) at regular time intervals using acomputer programmed to perform these calculations in order to obtain amore exact ratio, although 7.93 is a good approximation of this ratio.

B. Heating Rate of Target Cells Increased Relative to Non-Target Cells

In cases where the target cells and non-target cells have similardielectric constants, dissipation factors, specific heats, anddensities, or combinations thereof, the target cells and non-targetcells naturally heat at substantially the same or similar rates. Thatis, the ratio of the change in temperature of the target cells to thechange in temperature of the non-target cells as set forth in equation(184) is not large enough to be able to kill the target cells withoutdamaging the non-target cells. In accordance with the present invention,and as discussed in greater detail above, the heating rate of the targetcells relative to the non-target cells can be increased by introducinginto the treatment region a dielectric heating modulator (which may beor may not be associated with a targeting moiety) prior to theapplication of the dielectric field. The dielectric heating modulatorincreases the dissipation factor of the target cells. As such, uponapplication of the dielectric field, the target cells heat at a fasterrate than the non-target cells such that the target cells may beselectively killed.

Various methods may be used to determine the amount of dielectricheating modulator that is needed for a particular application. Forexample, with reference to equation (184), one skilled in the art willappreciate that the values for the dielectric constant, specific heat,and density of the target cells (with modulator) and non-target cellsare substantially the same in this case. That is, the difference betweenthe dielectric constant of the target cells (with modulator) compared tothe dielectric constant of the non-target cells is negligible, thedifference between the specific heat of the target cells (withmodulator) compared to the specific heat of the non-target cells isnegligible, and the difference between the density of the target cells(with modulator) compared to the density of the non-target cells isnegligible. As such, equation (184) may be simplified as follows:

$\begin{matrix}{\frac{\Delta \; T_{2}}{\Delta \; T_{1}} \cong \frac{{df}_{2}}{{df}_{1}}} & (256)\end{matrix}$

where

ΔT₁=increase in temperature of non-target cells in ° C.

ΔT₂=increase in temperature of target cells (with modulator) in ° C.

df₁=dissipation factor of non-target cells

df₂=dissipation factor of target cells (with modulator).

Thus, if it is desired to increase the heating rate of the target cells(with modulator) by a factor of X compared to the heating rate of thenon-target cells, then the dissipation factor of the target cells (withmodulator) must be X times greater than the dissipation factor of thenon-target cells. It is assumed that the dissipation factor of thenon-target cells is known (e.g., a value of Y). Thus, the dissipationfactor of the target cells (with modulator) must have a value that is Xtimes Y. It is possible to ascertain the dissipation factor of thetarget cells (with modulator) as a function of the amount of thedielectric heating modulator. For example, with reference to FIG. 12(discussed in greater detail below), a graph is provided in which thedissipation factor of ground beef liver mixed with nanogold is plottedas a function of the amount of nanogold. Using such a graph, therequired amount of the dielectric heating modulator may be determined byselecting the amount that corresponds to a dissipation factor of X timesY on the graph. Of course, other methods may be used to determine theamount of dielectric heating modulator that is needed for a particularapplication.

The value of X i.e., the factor by which, the heating rate of the targetcells (with modulator) is increased compared to the heating rate of thenon-target cells) will vary depending-on the types of target andnon-target cells. Preferably, the value of X is in the range of 1.5 to8.0, is more preferably in the range of 2.0 to 6.0, and is mostpreferably in the range of 2.5 to 4.0. Of course, one skilled in the artwill understand that there is a limit on the amount of dielectricheating modulator that may be introduced into a subject. As such, thereis a practical limit on the value of X depending on the subject and thetypes of target and non-target cells within the treatment region of thesubject.

The desired temperature of the biological targets compared to thedesired temperature of the non-targets at the end of the dielectricheating treatment will depend on the nature of the biological targetsand non-targets. For example, normal non-cancerous cells in the humanbody are typically maintained at about 37° C. (98.5° F.) while cancercells have a slightly elevated temperature of about 37.5° C. (99.5° F.)in the absence of any external heating. Normal non-cancerous cells arekilled at about 46.5° C. (about 9.5° C. increase in the temperature)while, cancer cells are killed at about 45.5° C. (about 8° C. increasein the temperature). At lower temperatures, cell death may occur in someof the cancer cells but not all of the cancer cells. It will also beappreciated to those skilled in the art that the temperature at which acell is killed depends on the time for which the temperature iselevated. The present invention, however, contemplates dielectricheating times of only a few minutes (e.g., 5, 4, 3, 2, or 1 minutes),and preferably for only a few seconds (e.g., 60, 50, 40, 30, 25, 20, 15,14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 seconds or less). Undersuch circumstances, the dielectric field is applied until thetemperature of the target cells (e.g., the cancer cells) is preferablyelevated to about 45.5° C. or more (e.g., about 46, 47, 48, 49, 50, 51,52, 53, 54, 55, 56, 57, 58° C. or more). Further, the dielectric fieldis applied so that the temperature of the non-target cells remains under46.5° C. (e.g. 46 45, 44, 43, 42, 41, 40, 39, 38° C. or less) during thetreatment. After the application of the dielectric field, the targetcells cool down relatively slowly, but are maintained at elevatedtemperatures long enough to kill most, and preferably all, of the targetcells. It will be appreciated that the dielectric field may also beapplied in a cyclical manner. For example, the dielectric field may beapplied for only a few seconds sufficient to bring the cancer cells to atemperature at which they will be killed. The cancer cells will thenundergo cooling from that temperature once the dielectric field isremoved. If the temperature of the cancer cells is not maintained abovethe temperature at which the cancer cells can be killed for a sufficientperiod of time, another round of dielectric heating may be applied inorder to increase the temperature of the cancer cells again. Such cyclesof dielectric heating may be repeated. Importantly, it is preferablethat the temperature of the non-targets cells will not reach atemperature for a sufficient period of time in which the non-targets arekilled.

As discussed above, in certain embodiments, the present invention isdirected to a method for selectively heating adipose cells in subjectsvia the application of a dielectric field. The treatment region containsboth adipose cells (to be killed) and non-target cells (which are notadipose cells). The desired temperature of the adipose cells at the endof the dielectric heating treatment is preferably about 46° C. or more(e.g., about 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58° C. ormore), and the desired temperature of the non-target cells at the end ofthe dielectric heating treatment is preferably about 46° C. or less(e.g., about 46, 45, 44, 43, 42, 41, 40, 39, 38° C. or less). In such anembodiment, the present invention contemplates dielectric heating timesof only a few minutes (e.g., 4, 3, 2, or 1 minutes), and preferably foronly a few seconds (e.g., 60, 50, 40, 30, 25, 20, 15, 14, 13, 12, 11,10, 9, 8, 7, 6, 5, 4, 3, 2, 1 seconds or less), depending upon thevoltage applied and the area and thickness of the adipose cells. If thetemperature of the adipose cells is not maintained above the temperatureat which the adipose cells can be killed for a sufficient period oftime, another round of dielectric heating may be applied in order toincrease the temperature of the adipose cells again. Such cycles ofdielectric heating may be repeated. Importantly, it is preferable thatthe temperature of the non-targets cells will not reach a temperaturefor a sufficient period of time in which the non-targets are killed.

Tests on the Temperature Effects of Dielectric Heating Modulators inFresh Ground Beef Liver or Solution

Tests were performed in which the test materials comprised ground beefliver alone or mixed with different amounts of several dielectricheating modulators. The beef liver was first ground, then mixed with anamount of a dielectric heating modulator using a ⅜″ Mini Micro tipattached to a Silverson mixer L4 RT-A. Other tests were performed inwhich the test materials comprised various dielectric heating modulatorsin a carrier solution having properties similar to the blood. Thefollowing dielectric heating modulators were investigated: (1) BlackPearl 2000 (Cabot Corporation); (2) Dynalyst 50KR1 (Cabot Corporation);(3) 10 nm gold particles; (4) 20 nm gold particles; (5) 50 nm goldparticles; and (6) glucose.

In each test, the various test materials were placed into a mold formedof silicone rubber with a polypropylene frame. The mold contained fourmolding cavities, with each cavity about 0.395 inches in diameter andhaving a depth of 0.525 inches. The frame was about 5.9×1.3×1.5 inches.The mold was placed inside a dielectric heater (Compo, Industries Model1025-L). One end of a fiber optic cable was inserted into the middle ofeach molding cavity (in each case, to a depth of about one-half thethickness of the test material), and the other end of each fiber opticcable was connected to a computerized temperature recording device(Neoptix Fiberoptic Temperature Sensor: Reflex-4 and NeoLink Pro Ver.1.3) using data acquisition software (NeoLink Pro Ver. 1.3). The moldwas closed, and the test materials were heated with a dielectric fieldhaving a frequency of 27.12 MHz, wherein the voltage between theelectrodes was 8,000 volts. The temperature of each of the testmaterials was monitored and recorded using infrared signals sent overthe fiber optic cables to the temperature recording device.

In a first test, the ground beef liver was mixed with various dielectricheating modulators to form mixtures having various concentrations,namely, 0.05 wt/wt % Black Pearl 2000, 0.1 wt/wt % Black Pearl 2000, and0.05 wt/wt % Dynalyst 50KR1. Three of the mold cavities were filled withthe test materials, and the fourth mold cavity contained ground beefliver with no dielectric heating modulator as a control. The results areshown in FIG. 8. As shown in that figure, the change in temperature wasabout 1.36 times faster than the control for the 0.05 wt/wt % BlackPearl, about 1.73 times faster than the control for the 1.0 wt/wt %Black Pearl, and about 1.81 times faster than the control for the 0.05wt/wt % Dynalyst 50KR1.

In a second test, the ground beef liver was mixed with varying amountsof glucose as the dielectric heating modulator to form mixtures havingvarious concentrations, namely, 5, 9, and 9.5 wt/wt % glucose (e.g., 5 gof glucose per 100 g of ground beef liver). The glucose was not added tothe ground beef liver in solution. Three of the mold cavities werefilled with the test materials, and the fourth mold cavity containedground beef liver with no dielectric heating modulator as a control. Theresults are shown in FIG. 9. As shown in that figure, the change intemperature was about 1.33, 2.64, and 2.52 times faster than the controlfor the 5, 9, and 9.5 wt/wt % glucose samples, respectively.

In a third test, the dielectric heating modulators comprised goldnanoparticles mixed in a carrier solution having properties similar tothe body to form mixtures having various, concentrations, namely, 0.0053wt/vol % of 10 nm particles and 0.005 wt/vol % of 20 nm particles (e.g.,53 mg of solid particles per 1 L of solution). Two of the mold cavitieswere filled with the two gold nanoparticle solutions (not mixed with anybeef liver), a third mold cavity was filled with distilled water, andthe fourth mold cavity contained ground beef liver with no dielectricheating modulator. The results are shown in FIG. 10. As shown in thatfigure, the change in temperature was about 4.81 times faster than theground beef liver for the 0.0053 wt/vol % 10 nm gold particles and about3.37 times faster than the ground beef liver for the 0.005 wt/vol % 20 mgold particles.

In a fourth test, the ground beef liver was mixed with goldnanoparticles to form a mixture having a concentration of 0.15 wt/wt %of 50 nm particles (e.g., 15 g of solid particles per 99.85 g of groundbeef liver). The 50 nm gold nanoparticles were provided in aconcentrated solution of about 1:3 wt ratio of solid to carriersolution. One mold cavity was filled, with the liver/nanogold testmaterial, and another mold cavity was filled with ground beef liver withno dielectric heating modulator as a control. The results are shown inFIG. 11. As shown in that figure, the change in temperature was about3.42 times faster than the control for the 0.15 wt/wt % 50 nm goldnanoparticles mixed with the ground beef liver.

Test to Determine the Dissipation Factor of Target Cells (withModulator) as a Function of the Amount of Modulator

In this test, the dissipation factor of ground beef liver mixed withvarying concentrations of gold nanoparticles as the dielectric heatingmodulator was' determined. A dielectric analyzer (HP 4291A RF Impedanceand Material Analyzer) was used to measure the dissipation factor ofeach test material at 37° C. The results are summarized in the followingtable:

Concentration of 10 nm gold nanoparticles (g of nanogold per Dissipation100,000 g of ground beef liver) Factor 0 1.65 2 2.64 5.3 4.62 10 7.58

This data is graphically shown in FIG. 12. For simplicity, it is assumedthat the dissipation factor of ground beef liver mixed with goldnanoparticles (as set forth in the table above) is comparable to thedissipation factor of cancer cells in the liver associated with goldnanoparticles. Of course, in practice, it would be desirable todetermine the dissipation factor of actual cancer cells with varyingconcentrations of gold nanoparticles.

It will be appreciated that the information shown in FIG. 12 can be usedto determine the amount of dielectric heating modulator required to heattarget cells (in this case, liver cells that simulate cancer cells inthe liver) to a predetermined temperature at which they will be killed(e.g., 50 C). It is assumed that the surrounding muscle tissue (whichhas a dissipation factor of about 2.25) will heat at the fastest rate ofall of the cell types in the treatment region. The muscle tissue shouldreach temperatures of no greater than 42.2° C. (108° F.); otherwise, thenormal muscle cells will be killed.

With reference to equation (256), the ratio of the change in temperatureof the liver cells mixed with gold nanoparticles (i.e., the targetcells) to the change in temperature of the muscle cells (i.e., thenon-target cells) is expressed by the following equation:

$\begin{matrix}{\frac{\Delta \; T_{l}}{\Delta \; T_{m}} \cong \frac{{df}_{l}}{{df}_{m}}} & (257)\end{matrix}$

where

ΔT_(m)=increase in temperature of muscle cells in ° C.

ΔT₁=increase in temperature of liver cells (with nanogold) in ° C.

df_(m)=dissipation factor of muscle cells

df₂=dissipation factor of liver cells (with nanogold).

It is assumed that the starting temperature of both the liver cells(with nanogold) and muscle cells is 37° C., that the desired temperatureof the liver cells (with nanogold) is 50° C., that the desiredtemperature of the muscle cells is 42.2° C., and that the dissipationfactor of the muscle cells is 2.25. As such, equation (257) can bewritten as follows:

$\begin{matrix}{\frac{50 - 37}{42.2 - 37} \cong \frac{{df}_{2}}{2.25}} & (258)\end{matrix}$

Thus, the required dissipation factor of the liver cells (with nanogold)is about 5.6. Using FIG. 12, one can determine that the dissipationfactor of the liver cells is about 5.6 when about 6.5 g of 10 nm goldnanoparticles are added to 100,000 g of the ground beef liver. Thus, theamount of dielectric heating modulator that should be added can bereadily determined. Again, it should be understood that the liver cellsin this example are used to simulate cancer cells in the liver (whichwould likely be the actual target cells in practice).

Test on Fresh Bacon

A test was performed in which the test material comprised a piece offresh bacon consisting of about 50/50 wt % meat/fat. The fatty portionand meat portion, of the bacon were layered on top of one another andplaced into a mold. A small piece of silicon-coated paper was placed onthe top layer of the bacon and the two layers were pressed together inorder to remove any air. The mold was placed inside a dielectric heater(Compo Industries Model 1025-L). One end of a fiber optic cable wasinserted into the middle of each of the meat and fat portions of thebacon (in each case, to a depth of about one-half the thickness of themeat portion or fat portion), and the other end of each fiber opticcable was connected to a computerized temperature recording device(Neoptix Fiberoptic Temperature Sensor: Reflex-4 and NeoLink Pro Ver.1.3) using data acquisition software (NeoLink Pro Ver. 1.3). The moldwas closed, and the bacon was heated with a dielectric field having afrequency of 27.12 MHz, wherein the voltage between the electrodes was8,000 volts. The temperature of the meat and fat portions of the baconwas monitored and recorded using infrared signals sent over the fiberoptic cables to the temperature recording device. The following tableidentifies the temperatures of the meat and fat portions of the bacon atspecific time intervals:

Time (sec) Meat Portion (° C.) Fat Portion (° C.) 0 37 37 0.6 38.2 43.61.0 39.3 51.5 1.4 41.9 65.2

These results are graphically shown in FIG. 13. Thus, in 1.4 seconds,the change in temperature of the meat portion was 4.9° C. (41.9-37) andthe change in temperature of the fat portion was 28.2° C. (65.2-37).Also, the ratio of the change in temperature of the meat portion to thechange in temperature of the fat portion was about 5.76 (28.2/4.9). Inother words, the fat portion heated about 5.76 times faster than themeat portion. It can be appreciated that the fat portion heated at afaster rate than the meat portion due mainly to the relatively lowdielectric constant of the fat in comparison to the relatively highdielectric constant of the meat. Further, the fat portion has a lowerspecific heat and a lower density compared to the meat portion so thatthe fat portion takes less energy to heat. The dissipation factor of thefat portion is lower which will slow down the rate of heating, butoverall the fat portion still heats faster than the meat portion asdiscussed above.

While the present invention has been described and illustratedhereinabove with reference to various exemplary apparatuses andmethodologies, it should be understood that various modifications couldbe made to these apparatuses and methodologies without departing fromthe scope of the invention. Therefore, the invention is not to belimited to the exemplary apparatuses and methodologies described andillustrated hereinabove, except insofar as such limitations are includedin the following claims.

1. A method for selectively heating adipose cells in a subject via theapplication of an alternating electric field, comprising: positioning atreatment region of said subject between a first electrode and a secondelectrode, wherein said first and second electrodes are connected to agenerator operable to apply an alternating electric field between saidelectrodes, wherein said treatment region contains said adipose cellsand non-target cells; activating said generator to apply saidalternating electric field between said first and second electrodes andacross said treatment region to thereby heat said treatment region; andwherein said adipose cells heat at a faster rate than said non-targetcells within said treatment region.
 2. The method of claim 1 whereinsaid treatment region comprises a portion of a human body.
 3. The methodof claim 1 wherein said adipose cells are located in a treatment regionselected from the group consisting of said subject's abdomen, buttocks,thighs, arms, and chin.
 4. The method of claim 1 wherein said adiposecells are located in a treatment region selected from the groupconsisting of said subject's dorsocervical area or submandibular area.5. The method of claim 1 wherein said activating step results in thekilling of said adipose cells.
 6. The method of claim 1 wherein saidactivating step results in said adipose cells being heated to about 46°C. or more while said non-target cells are heated to less than about 46°C.
 7. The method of claim 1 wherein said activating step results in saidadipose cells being heated to about 50° C. or more while said non-targetcells are heated to less than about 40° C.
 8. The method of claim 1wherein said activating step occurs for about 4 minutes or less.
 9. Themethod of claim 1 wherein said activating step occurs for about 20seconds or less.
 10. The method of claim 1 wherein said alternatingelectric field is generated at a frequency in the range of 1 MHz to 100MHz.
 11. The method of claim 1 wherein said alternating electric fieldis generated at a frequency of 27.12 MHz or 40.68 MHz.
 12. The method ofclaim 1 wherein a substantially constant voltage is provided betweensaid first and second electrodes.
 13. The method of claim 12 whereinsaid generator is operable to generate a signal that is substantially asinusoid having a wavelength λ, and wherein said treatment region ispositioned between said first and second electrodes and adjacent a pointon said first electrode that is located a distance of ¼λ or ¼λ plus amultiple of ½λ from said generator such that said substantially constantvoltage is provided between said first and second electrodes.
 14. Themethod of claim 1 wherein a substantially constant current passesbetween said first and second electrodes and through said treatmentregion.
 15. The method of claim 14 further comprising displacing any airlocated between said treatment region and said first and secondelectrodes with one or more flowable materials that allow saidsubstantially constant current to pass between said first and secondelectrodes and through said treatment region.
 16. A method forselectively heating adipose cells in a subject via the application of analternating electric field, comprising: positioning a treatment regionof said subject between a first electrode and a second electrode,wherein said first and second electrodes are connected to a generatoroperable to apply an alternating electric field between said electrodes,wherein said treatment region comprises a portion of a human body thatcontains said adipose cells and non-target cells; and activating saidgenerator for about 2 minutes or less to apply said alternating electricfield between said first and second electrodes and across said treatmentregion to thereby heat said adipose cells to about 50° C. or more whilesaid non-target cells are heated to less than about 40° C.
 17. Themethod of claim 16 wherein said adipose cells are located in a treatmentregion selected from the group consisting of said subject's abdomen,buttocks, thighs, arms, and chin.
 18. The method of claim 16 whereinsaid adipose cells are located in a treatment region selected from thegroup consisting of said subject's dorsocervical area or submandibulararea.
 19. The method of claim 16 wherein said activating step results inthe killing of said adipose cells.
 20. The method of claim 16 whereinsaid alternating electric field is generated at a frequency in the rangeof 1 MHz to 100 MHz.
 21. The method of claim 16 wherein said alternatingelectric field is generated at a frequency of 27.12 MHz or 40.68 MHz.22. The method of claim 16 wherein a substantially constant voltage isprovided between said first and second electrodes.
 23. The method ofclaim 22 wherein said generator is operable to generate a signal that issubstantially a sinusoid having a wavelength λ, and wherein saidtreatment region is positioned between said first and second electrodesand adjacent a point on said first electrode that is located a distanceof ¼λ or ¼λ plus a multiple of ½λ from said generator such that saidsubstantially constant voltage is provided between said first and secondelectrodes.
 24. The method of claim 16 wherein a substantially constantcurrent passes between said first and second electrodes and through saidtreatment region.
 25. The method of claim 24 further comprisingdisplacing any air located between said treatment region and said firstand second electrodes with one or more flowable materials that allowsaid substantially constant current to pass between said first andsecond electrodes and through said treatment region.